Right off the bat, I can say I'd like the text that shows how many coins each item costs to not be blacked out as it makes it very hard to read, at least without bumping my brightness up. It stops me knowing what I'm aiming for and makes the game feel pointless until I hit an arbitrary point of being able to earn something - which isn't the case, so visibility is quite important.
10 coins seems like it should feel like a small amount to buy Palms (what I can gather being always the first to become available), but in practice it felt ever so slightly too high. I think it's because that first piece of the game is literally just walking around an empty world picking up coins. Once some variety appeared with the trees it was a much better experience, but getting to that point should probably come a little faster.
The object physics is nice, I like how shooting things pushes even coins around, it feels like a world I can really do things in. Picking things up was ALMOST annoying, however, as the collision boxes seem to be the tiniest bit too small. Occasionally I'd just spin a stick around instead of pick it up, and sometimes (but rarely) I'd actually push a coin away instead of picking it up. That might have something to do with what it's colliding with depending on how the player object is set up, but I won't pretend to know how you do your thing.
There is one issue with shooting objects wherein if there was a bunch of pickups together against something else, shooting them and pushing them against the wall would result in the 'bullet' getting stuck and joining the pile until it disappeared. Again, not to assume how your game works, but the bullets seem to only 'explode' when they collide with certain objects and that doesn't include pickups. This works just fine, but can result in the bullet getting stuck in place when the things it's trying to push out of the way can't move due to obstacles. Maybe a check for whether the bullet is moving or not to see if something's stopped it, and explode if it has?
Attacking takes a slightly too annoying amount of time to recharge, especially given trees (the first things that can be bought) take two hits. I understand recharge times for combat with enemies, but for gaining resources it feels more sluggish. This got easier with the wooden sword of course, which seems to shorten the cooldown, but cutting down trees was still a bit annoying. Maybe making recharge times shorter if you're attacking resources, or shorter overall with more hits needed for certain things to balance it out? Having to attack three times to cut down a tree would feel much better than two if I got to attack it faster, even if it would require more action on my part since it would still feel like I'm doing something.
The animation for the weapon could do with a little tweaking too, the linear movement doesn't feel quite right. The sprite shrinking looks good, maybe add another dynamic element to its movement. A visible representation of the cooldown might be a nice addition too - maybe along the lines of the reticle?
I honestly forgot about the crafting aspect since I forgot you could check your inventory, and wasn't aware the crafting menu was in the inventory. Perhaps a reminder on the UI (an inventory icon with the control that opens it?) and a mention even just on the controls page that the inventory screen is also where crafting is. In regards to crafting, too, I noticed the items I could craft didn't mention the materials I needed and had to figure it out based on what I lost when I made them. It wasn't always clear what requirements I needed to make possible items show up, either - the sword made sense, but at one point I noticed I could create armor and have no idea why. Re-checking the shop, I see it had appeared in my 'craftables' section so I must have bought something to unlock it, but I suppose I overlooked it because the sprite doesn't really read as armor. Once I made it, it disappeared from my crafting menu anyway.
My guess is things only appear in the table when you have the materials to craft them. The issue with that is I have no idea what to aim for if I know I'm able to craft SOMETHING. If this is intentional, then making the mystery of it a part of the mechanic would go down better than leaving it genuinely a mystery. Maybe craftables are always shown on the table but are greyed out if you don't have the right materials, and recipes are shown but only as "???" until you successfully craft an item, after which the recipe would be shown. The success of 'obtaining' the recipe would act as something else the player can feel like they achieved (and another thing to populate the menu with, not unlike the world), and wouldn't feel like they're blindly stumbling through a series of choices of what to buy and make - we're already wandering a world with no idea where we're going, having that element in every aspect of the game would make for a sort of unity but not an enjoyable experience.
The ramping up of coin rewards was great, I always felt like I was reaching a new level of resource gaining when I discovered and broke more things. Rocks were a revelation. Frogs seemed a bit overpowered for how early they were introduced which led me to save up to purchase more health before unlocking anything else, and once I had a little more it felt like a good fit. It was good in the sense that it was a choice to make and reaching the point of making it (200 coins) and getting on their level felt like a great reward, but given how most of the other purchase options were stronger enemies, it was the much better option. It felt like a choice at first, but it wasn't much of one. Maybe buying your first extra heart is cheaper, then the price increases each time you buy one? Or different merchant instances have different prices, giving another choice for the player (buy now or look for a cheaper one).
Armor being destroyed practically instantly after attacks felt a bit unfair, since I have to remake it every time. It looks like armor takes damage instead of your health, which makes all armor single-hit defences since wood only defends against the smallest possible damage and by the time you unlock stone armor you're fighting frogs that deal whole hearts, the same amount stone defends against. Having to recreate armor after every other fight (unless you're good, I guess) got annoying, and I even forgot to do it most of the time since I wasn't used to the mechanic of having glass shields given how they work in most other games. This isn't to say that doing something differently to most games is bad, not at all, it just didn't feel particularly enjoyable the way it currently works.
Ironically, the random nature of the game makes the map feel a little same-y. If you want to find literally anything, just walk in a direction until some spawns. Everything seems to spawn at different rates which is good, but that randomness is spread over the whole map. I hate to make the reference, but it's like if every kind of tree, mob and block type spawned in every biome (and height) of Minecraft. Areas of some things being more common than others would lead to the map feeling less like a randomly generated desert and more like a world to be discovered, since finding clusters of things amid areas where some things are rarer would feel more like a lucky discovery than a discovery based on luck.
Some way of knowing where you've been might be nice so you know where you can go to find new things - a map, perhaps? Unless not knowing where you're going is part of the experience, though in a desert world it does feel a bit less like exploration and more like just finding the next thing.
I played for over an hour while writing these notes and I have to say I'm having a good time, I'm ramping up gradually and feeling ready to take on bigger enemies, saving up for more health - the price of unlocking enemies seems to suggest the game thinks I'm ready to take on stronger things but I know for a fact I need more health for any of that. This means I have something to work towards, though, and that's good - it's just a question of balancing the mechanics that are there, because at it's core this is a pretty fun experience that I'd like to see developed more.