Google Nest and Google Home speakers and displays will automatically use the same YouTube music account that is linked with the Google account on the devices.
Try adding your new Google account as a user or reset your devices and set up again with the Google account that you have a music subscription with.
Did you try the steps Cathal_S suggested? I understand if you're going to try another solution, but I would love to be able to help you get things working without you having to buy new equipment. If you've already made the switch or if you would like to troubleshoot this a bit more, let me know and I'll be happy to help out here.