will time machine backup to ssd on wifi

It's not supported by Apple, but if the router uses a SMB implementation with the Time Machine over SMB specification, then it might work. In general, if the router supports SMB3, it will likely be running an SMB implementation that does support the Time Machine over SMB specification. If it says it runs Samba for SMB, then any version after 4.8 should support Time Machine over SMB.

I do it with the SSD hosted from an M1 Mini.

What do you have to host the SSD?