[PROBLEM] SSD Media / System Partition Issues

[Nutul]

but I did use Balena Etcher from memory.

I am not familiar with it, but if it allows the same level of pre-configuration you should be good to go.
If any blocked / inaccessible functionalities in the UI arise, especially in the configuration pages, that's a signal the image has not been configured as it should (hence, re-do it with RPi Imager)
Then, place all your music in the new partition, at least under a "Music" folder, and from within moOde, do a Library update.