If you do a search you probably would find lots of pertinent information.
The 13" 2015 MBP is on its last leg on being able to upgrade to the current macOS. There is no way I can upgrade my 2008 MacPro and 2012 MBP to Big Sur without major major hassles. They are in Catalina already.
The original 13" 2015 MBP came with 128GB of SSD. This certainly on the meager side. I changed the battery a few months ago after it started to bulge.
I gathered 3 items to do the upgrade.
1. The Rongdeson M.2 NVME SSD enclosure
2. SPG SX8200 PRO 512GB
3. Sintech NGFF M.2 adapter card
I didn't bother to backup anything on TimeMachine or otherwise. Just do it.
Put 2 into 1. Connect to the MBP, erase the new SSD into APFS and the rest default values.
Upgrade the MBP to Big Sur by downloading and installing on the new SSD
The upgrade will prompt you for anything it needs and it also prompts you to migrate your existing Mac to the new Mac, ie copy the old SSD data to the new SSD.
After the migration, the last step is to turn off the MBP, open the bottom cover, unplug the battery, remove the old SSD. Remove 2 from 1. Then slide 2 into 3 completely. Take 3 with 2 attached and plug 3 into the existing slot, make sure they are inserted all the way. It's like at an angle, seat it and screw it down. Plug the battery. Put the back cover back on and the screws.
Turn on the MBP, answer a few prompts like verify your Apple ID and stuff. That's it.
