Why would you have to reformat your SSD drive you install? That literally defeats the purpose of having the extra hard drive. You should be able to use it on any PS5 and transfer data and such. That's like saying you have to reformat an external hard drive everytime you plug it in to a new computer.
This happened on an storage upgrade I did on my original PS5. Did a clone of the drive and it still forced a format. It looks like they might have finally updated this to avoid this issue. The exteranal drives don't run into this problem though.