Hi Gavin,
I'm afraid I'm not completely up to date on the iPhone 13, but I don't believe you should have any problem with replacing the earpiece speaker. On previous models (X through 12), the earpiece speaker was part of the front sensor assembly on the display. With a little bit of soldering, it was possible to replace that speaker without affecting Face ID; it was the replacement of the full assembly that disabled Face ID.
With the iPhone 13, the earpiece speaker is no longer part of the sensor assembly; it is a separate, replaceable piece all by itself. So unless Apple has specifically added pairing to the speaker (which I have no knowledge of), I can't see any issue with putting in a new speaker. In either case, there's no reason it should affect Face ID.
As far as the screen, there's a note on the screen replacement guide that addresses that issue.
[quote]***Note:*** True Tone and auto brightness functionality is disabled after a screen replacement, even when using an original Apple screen. Face ID is also disabled, unless the iPhone is running iOS 15.2 or newer.[/quote]
It appears Apple started out disabling Face ID when the screen got replaced, but as of iOS 15.2 they relented. So as long as you make sure to update to 15.2 or later, you should be fine with replacing the screen. Of course, without transferring data from the old screen to the replacement, it will still turn off auto brightness and true tone; you need a programmer to read and write the data. If you know a repair shop you may be able to talk them into doing that data transfer for you, hopefully for a minimal cost, or you can buy a programmer; the one I just ordered cost about $85 USD.