I typed this up and then remembered an old game called chip's challenge. Found a link to some gameplay and realized how much it influenced my expectations of these games. I'll include the link at the bottom but some of its features wouldn't work well in this game.
I'm a bit colorblind so the brown(?) bridges are a little tricky to distinguish from the background green. Otherwise, this was a fun start.
Some ideas you may be interested in.
- Teleports/portals
- Directional tiles
- can only go one way or
- changes the object's course
- switches
- Lower walls
- Raise/close floors to complete paths
- key items
- batteries or some other move limiter
- keys/crystals/whatever required to make it through an obstacle
- keys/crystals/whatever that must be gathered before leaving
- enemies
- Move around the map in predictable patterns
- multiple types
- turns left at edges
- turns right at edges
- floats around the outside wall
- just moves in a specific square pattern
I'm sure there's a million more ideas but these are the only ones I could think of in these types of games.