I also had this problem. Since my native Apple apps worked with the carplay microphone I guessed it was Google Maps specific so I posted here as well
https://support.google.com/maps/thread/137359516/seems-like-google-maps-isn%E2%80%99t-using-car-microphone-with-apple-carplay-on-ios-15?hl=en
Anyway, after verifying that Google Maps had access to the microphone because it was working fine up until recently I thought maybe reinstalling would work and it did, but it took a couple of tries. Here's what didn't work and what did work for me
1. Didn't work
Uninstalled Google Maps.
Turned iPhone off
Turned iPhone on
Installed Google Maps
Launched Google Maps
Glimmer of hope. It asks for permission to access location , microphone, and contacts.
I'm able to give access to microphone and contacts but not location. If go
to Settings -> Privacy -> Location Services Google Maps isn't
listed (Google Calendar is, but not Gmaps).
Turn iPhone off
Turn iPhone on
Google Maps appears in Settings -> Privacy -> Location Services and I grant it access
Test with microphone using CarPlay is unsuccessful
2. Did work.
Uninstalled Google Maps.
Turned iPhone off
Turned iPhone on
Installed Google Maps
Turned iPhone off
Connected USB cable in car for CarPlay
Turned iPhone on
Launched Google Maps
Am able to grant access to location services, microphone, and contacts
Tests using microphone in car seems to work. Will continue to test and validate.