I have a new pair of Edifier R1700BTs speakers. Google Home mini will see the speakers, give an audible tone through the speakers, and then give a can't connect error.
I've tried a soft reboot of Google Home mini, a hard reboot, and a complete factory reset... the same issue each time.
From Google Home app, I'll select my Google Home mini device --> Settings --> Audio --> Default music speaker --> Pair Bluetooth speaker. Google Home app will scan, find the speakers, select the speakers and then fail to connect.
I know how difficult this is for you — let's see what's going on.
Have you tried reinstalling your Google Home app? Could you also try rebooting your Bluetooth speaker and router to refresh the connection. Once done, try saying "Ok Google, clear all paired devices".
Let us know how it goes.