Hey, I know that compose is in alpha, but I want to use it in a personal project for a basic Cart & Inventory app. Is that possible with the current state of the project? Can I use swing components if I need some use case that is not supported yet?

Is it possible? Probably. This question is the type where it will get tons of "it depends" responses. Personally, I wouldn't feel comfortable using compose on android, let alone on desktop

Can I use swing components if I need some use case that is not supported yet

Using Swing components inside Compose isn't supported now. You can only use Compose inside Swing component (https://github.com/JetBrains/compose-jb/tree/master/tutorials/Swing_Integration) Theoretically you can place Swing component over

ComposePanel

and adjust its position. Also you can open Swing window/dialogs/native file choosers from some Compose callback.