The Picade Hat shop page says * Compatible with all 40-pin Raspberry Pi models
That’s the current USB C version, hardware wise, I would think your hat will work with a Pi 4. The GPIO header pinout is the same. Assuming you don’t exceed the 2.5A limit of the older model power supply. I have run a Pi 4B on the 3B supply with an adapter with no issues.
That being said, software wise, your more likely to be caught out by the installer not liking the latest and greatest Pi OS release.
If that happens you can get older versions of Pi OS / Raspbian here. Index of /raspbian/images (raspberrypi.org)
Any Pi with a 40 pin header should work fine. The micro-B Picade X HAT will only supply your Pi 4 with 2.5A though, so you might find that you need to power the screen/Pi separately if you run into power issues.