phone fell in water

The first thing you have to do is stop USING THE PHONE, turn it off, and leave it off until you can properly clean it. Running the phone with liquid only hurts your chances of being able to save it!

Water got into the phone, at least in your case; the back glass being broken voided your liquid resistance, and did it in. That said, sometimes you get lucky and the phone can be fully repaired. Refer to this guide or this guide and see if you can clean the motherboard and modules like the FaceID camera (if they're dead you need to get an interposer board and replace them, assuming there's enough life left to get the calibration data off of them for it to work; otherwise FaceID is gone). If you can't recover the phone enough to make it reliable liquid damage is generally a BER repair since the phones often need multiple replacement modules to be properly repaired. The odds of truly being able to save the phone are slim (especially when you add things like pool chemicals to the mix!!!), so you have nothing to lose by trying once the phone gets dropped in liquid, especially a pool. That said, your screen is probably toast; even then, save it so you can move your TrueTone data which can be cloned over to a replacement display with a tool like the iCopy.

Your best bet to save the phone if you can do this is to clean the camera modules as much as you can and hope they still work as they are paired to the logic board. As far as the battery goes, don't save it beyond saving it ENOUGH to clone the encrypted data from the old one to the new battery if you want to save the battery health feature. If you do not care you can safely dispose of it.

My strong recommendation with this phone considering the risk of permanent long-term failure due to being dropped in a pool is fix it enough to recover the phone so you can use it in the meantime but also backup your data if need be. Once you accomplish this, you really should look for a used 13. It shouldn't be hard to find a nice 13/13 Pro 256/512GB used with preorder season for the new phones, even factory unlocked. AS LONG AS THE PHONE IS FULLY UNLOCKED (by the carrier or sold that way by Apple) you can move your SIM card if it isn't damaged (though some carriers will require you to swap the IMEI# out on their system; but this is generally a Verizon "feature"; maybe T-Mobile too now due to how poor their network security is). You'll pay for the fully unlocked status (especially if it came from Apple like that) but it's worth it by a long shot, especially with carriers like T-Mobile who fight against unlocking used phones.