Flash isn't working

As nearly as I can tell, the flash on your phone is mounted on the back side of the motherboard cover. Here's the part I'm referring to.

It appears to be fastened with just adhesive, so replacing it should simply be a matter of removing the cover, flipping it over and prying it off. Follow the Battery Replacement Guide up through Step 19 to take it off.

Motorola Moto G 5G (2022) Battery Replacement - iFixit Repair Guide

Note that I believe you can skip Step 16, removing the power button, but I'm not sure whether you actually need to disconnect it in Step 15 or not.

Again, I believe the flash is mounted on the back side of the motherboard cover so you should be able to get to it once you have the cover off. Here's what it should look like.

Here's an example of an eBay listing selling the part; this isn't an endorsement but just an example of what you're looking for. An internet search should turn up more choices for you.

Flash Board for Motorola Moto G Stylus 5G 2022 Genuine OEM Replacement Replace - eBay

Assuming you've tried software solutions like restarting your phone and even worst case restoring it to factory settings, replacing the flash would be the first step I'd try to fix it. While you have it out, check the spring contacts on the motherboard to make sure they're not bent down and failing to make contact with the flash board. You might want to try cleaning them with a pencil eraser and/or 90% or higher concentration isopropyl (rubbing) alcohol before replacing it though.

Good luck, and let us know what you find and how it all turns out; your experience could help the next person who comes along with the same problem.