I'm sorry to hear about your Nest Mini not playing music from Spotify ― a few questions: have you tried playing through YouTube Music? How was it? It would help a lot if you could do a sequential reboot first. Unplug the power cord of your router followed by your Nest Mini. Plug them back in after 3 minutes or 5 minutes tops. Restarting your phone might also help.
Tell me how it goes.