Mooncloud Lake is a thematically rich world, so it's getting three mechanics instead of two. Its main mechanic goes with the "moon" part: Phases. A door can have multiple "phases", and there are collectible items called Moonstones that, when collected, cause all doors that have phases to move to their next phase. For example, if a door's phases are Red 3, Blue 5, and Purple -1, then it starts as a Red 3 Door, becomes a Blue 5 Door when a Moonstone is collected, becomes a Purple -1 Door when another Moonstone is collected, returns to being a Red 3 Door when a third Moonstone is collected, and repeat. Keys and Scanners may also have phases as such, but Keys, Doors, and Scanners cannot transform into each other in Phases - an object with Phases will still always consistently be one of those three. Moonstones don't go in your inventory when collected, they just cause their phase change and disappear. Moonstones may have a number (to increment Phases by multiple, or go backwards if negative), and if Blueprint then they set all Doors to whatever Phase they'd be in if that many Moonstones had been collected so far. Star and Unstar Moonstones exist, so while Moonstones are Starred, Phases cannot change.
Its secondary mechanic, going with the "lake" part, is Filters. These are like doors, but their costs are not in Keys. The primary type are Water Filters, which cost Buckets of certain colors. There can also be Seed Filters, Spirit Filters that cost specific Spirits, or Spirit Filters that just have a number of Spirits to spend (in this case you may choose which of your Spirits to lose). Filters, of course, are themselves immune to Buckets. Scanners were already able to scan for non-key items as their requirements (and already have been doing so for Spirits), though perhaps they haven't started doing so for Buckets and Seeds until now. (Yes, Filters can be Mechanical)
The last mechanic in Mooncloud Lake is more of a side mechanic: Clouds, to go with (of course) the "cloud" part. A level can now consist of multiple "elevations", where each elevation is basically a separate room. When you're touching a cloud, you can choose to use it, but you don't have to. White clouds take you up in elevation when used, and dark clouds take you down in elevation when used (clouds have numbers next to them that tell you how far up or down they go. Clouds do not disappear when used, so they can be reused if you return to their elevation. Objects only take up one elevation, though it's possible (but rare) for an object to take up the same position on multiple elevations at once. Since this is meant to be a side mechanic for now, in this world clouds always come in white-dark pairs, so the mechanic doesn't do anything yet other than essentially add a third spacial dimension to levels (with specific "ladder" points, the cloud pairs, to travel up and down the Z-axis in discrete steps).
Etchstone Cliff's first mechanic is Etches, stone-etching tools that are another collectable item. If you have a nonzero amount of Etches, you can spend all of them at once to etch their number into a door or filter, changing that door's lock number to match the amount of Etches you had. There can be multiple colors of Etches - these colors have nothing to do with the colors of doors, and they all act identically (sprite-wise it's probably just their handles that change), it's just that Etches of different colors are stored separately in your inventory, thus they're used up separately, so you can be carrying multiple potential numbers. Filters may cost Etches. Starred Doors are immune to Etches.
For the "cliff" part of the world, the elevation mechanics that were introduced in Mooncloud Lake are fully realized here: now the clouds don't always come in pairs, so your way down isn't always the same as your way up. There are also Collapsing Clouds, which are like regular Clouds but they disappear after being used once.
Lockpick Library's first mechanic is Logical Scanners, which means Scanners' conditions can now include multiple "locks" with AND, OR, and NOT statements. (In the "themes inspire mechanics" context, this comes from the fact that in a library you read whole books instead of single statements). Blueprint applies to individual "locks" rather than the Scanner as a whole. Spirits have Scanner-like conditions, so their conditions can also be these logical statements now.
Combo Doors fit with Lockpick Library's theme perfectly, so if I was going to add them at all I'd keep them here, but they're not really needed - Doors aren't as important in this game as they are in canon IWL, generally Keys and Scanners are more important here. But without Bicolor/Combo Blast Sacrifice Doors, how will Theme-Mechanic Converse pull off the more math-y things that canon IWL does? Well, this library has some math textbooks in it too, which means Operator Keys are introduced this world. For those who don't remember Operator Keys from the museum, they allow Keys to do math things other than adding or subtracting constants (or setting Key counts to a particular value), such as multiplying your Orange Key count by 3, or adding your Cyan count to your Purple count.
Mechanical Nexus's primary mechanic, based on the "Nexus" part of being where all the doors are made, is Dispensers. Dispensers have an ordered list of objects within them (these may be any object - Keys, Doors, Buckets, Scanners, Messes, Spirits, Seeds, Moonstones, Filters, Clouds, Etches, Shelves, other Dispensers, etc., and they need not all be the same type). When the level starts, each Dispenser dispenses its first object into the level. The Dispenser then remains inactive until the object it dispensed is collected, destroyed, etc. (the object needs to no longer be present), then it waits until Lily is no longer in its range nearby it (different Dispensers can have different ranges), at which point it dispenses its next object, and repeat. Normally a Dispenser disappears once its object list is exhausted, but some Dispensers then have a second cycle of objects that repeats infinitely after its first list is exhausted.
Mechanical Nexus's side mechanic, based on the "Mechanical" part, is Gears, a collectable item used to mess with Mechanical Doors/Scanners/Filters. A positive Gear. A positive Gear may be spent on a non-Mechanical, openable object like a Door, Scanner, or Filter when you open it to cause that object to close back up after you cross it, as if it was Mechanical. It doesn't actually become Mechanical, though, it just re-closes the one time. A negative Gear may be spent on any Mechanical object to interfere with the gears in its mechanisms, grinding it to a halt and thus making it no longer Mechanical. You have to be able to open the object in question to use a Gear on it, so using a Gear on a Mechanical object therefore opens it permanently (for Doors and Filters it still spends its spending that one time, it just doesn't reform afterwards). Filters may cost Gears, but this does not make them immune to Gears (but Starred objects are immune to Gears).
The Miracle Tower's first mechanic, to go with the "miracle" part, is Spiritual Blessings and Curses, an expansion of the Spirits mechanic: Spirits can now have a "blessing" (an effect they cause when you collect them) and a "curse" (an effect they cause when they leave). Usually these effects are just giving you some amount of keys or other item (positive or negative), though there might be other effects they could cause, such as incrementing Phases or applying the effect of an Operator Key. Also, the condition for a Spirit being collectable can now be different from the condition that you have to meet for it to stick around once you have it. If you meet its collection requirement when you collect it but not its staying requirement, it immediately leaves when you collect it, giving you both its Blessing and its Curse immediately. A Spirit can also have a third effect, a "Summoning" (these can do the same things that Blessings and Curses can), and there's a new pickup type called Spirit Boards (like an Ouija Board), which when collected cause all Spirits currently haunting Lily to trigger their Summoning effect.
The "tower" part warrants a further expansion of the elevation mechanics: it's now possible for objects to stretch across multiple elevations at once (so a door could take up the same position across multiple elevations, and if you destroy it on one elevation it's destroyed on all of them), and "your elevation changes by a particular amount" is a possible Spiritual Blessing/Curse/Summoning.
With Buckets and Etches in play, Chromatic Monolith probably has a good bit of door editing involved, making it somewhat of a mix of the canon Chromatic Monolith and the canon Bridge to New Memories: Scanners are probably the things you need to get past to make progress, and you edit and recolor doors to make the right setups to let you get past them.