Setting up Time Machine with Internet & Google Nest

I'm trying to set up my Time Machine to backup my desktop Mac and laptop MacBook Pro in a new home with Cox Internet. I had been able to set everything up in our previous home (Mediacom internet) to back-up both our computers wirelessly using an ethernet connection between the Time Capsule and Mediacom router and using our Time Machine as a router as well as a backup using Bridge Mode (I think). Our latest home is much older (thicker walls), so we need boosters in some rooms for a stronger signal throughout, and decided (based on a suggestion from our internet provider) on Google Nest to provide this function. The problem is Google Nest also acts as a router (but not as a backup), so now we have TWO routers going (presumably). I have attempted to reconfigure the Time Machine to use our new local network. The Time Machine seems to be providing regular backups for our main (desktop Mac), but is not providing backups for my MacBook Pro. Does anyone have any suggestions on how to use the Time Capsule to just provide a wireless backup function for both of our computers while using Google Nest as a router? Or is my only option to ditch the Google Nest boosters and go back to using the Time Machine as both a router and backup?