Used Yast2 Partitioner GUI to create and mount a partition, but user has no write permissions. What next?

It is hard to tell, where you took the wrong turn and which action led to a loss of your home partition. I get the feeling (as you did not tell us explicitely) that your goal was to move your home partition from btrfs to ext4?

Because already in this comment can be seen that you don’t have any btrfs home partition.
That is why i asked to inspect the content of the new partition.. Maybe you only renamed the mountpoint and everything is still there.

Normally it is straight forward to add an external drive with the YaST partitioner. Maybe you have choosen the wrong drive/partition to edit and accidently overwrote a valid conbfig.