Generally we don't replace microphones; rather, it's done by replacing the assembly that holds the microphone. In this case it's the entire rear charging coil/flash/microphone assembly. Note that on the iPhone 15 models, the charging coil is paired to the motherboard, so you will receive a genuine parts warning if you replace it with an aftermarket part (such as those sold by iFixit). You can install a used genuine Apple part and the Repair Assistant will allow you to pair it to your phone, as long as it wasn't taken from a phone that has been reported as lost or stolen. To the best of my knowledge, you shouldn't lose any functionality, but you will have to live with a permanent badge on your Settings icon indicating the non-genuine parts warning. If you're confident in your soldering skills, you may be able to purchase an aftermarket part and salvage the microphone from it for use on your original coil; otherwise you'll have to replace the complete assembly.
So yes, you're definitely on the right track as to what steps you should take. As far as guides go, I didn't find any written iFixit-style guides, but there is a pretty good YouTube video available showing how to replace the charging coil.
iPhone 15 Pro NFC Wireless Charging Coil and Flashlight Flex Cable Replacement - YouTube
You can get halfway there with the iFixit Back Glass Replacement guide if you want.
iPhone 15 Pro Back Glass Replacement - iFixit Repair Guide
Personally, I would go with your instincts and open up the phone to clean and check the microphone's access hole. 90% or higher concentration isopropyl (rubbing) alcohol is a good choice to clean it out, as it won't leave any residue. You can follow the first part of the video to dismount the flash then the microphone and stop there to do the cleaning. If you end up having to replace the mic, then the rest of the video will show you how.