Can I recover data from a Macbook Pro (2015) caught in a boot loop?

My Macbook Pro (2015) is generally stuck in a boot loop. When attempting to start it, I see the Apple logo and a progress bar but it restarts before the progress bar is complete.

I can shut it down and, with persistence, get into Recovery Mode (although attempting this often leads back to the boot loop when the progress bar below the globe image is complete).

In Recovery Mode, sometimes I see the 'Macintosh HD' and 'Macintosh HD - Data' volumes and can run First Aid successfully on both. Other times, First Aid has failed on 'Macintosh HD' (when shown under 'AppleAPFSMedia' and without 'Macintosh HD - Data' visible) with 'Storage system check exit code is 8' shown in the details. On other attempts, First Aid has also failed on a volume titled 'Update' that is visible sometimes.

Attempts to reinstall the macOS have led back to the boot loop and, unfortunately (foolishly), I do not have a Time Machine back up.

I can also get into Target Disk Mode, connecting to a Macbook Pro (2012) running Catalina, but when I've done this the only drive visible on the 2015 Macbook Pro is titled 'Update'.

I've tried everything that I have found through much 'Googling' (except physically removing the drive) and have basically given up trying to get the 2015 Macbook Pro out of the boot loop. It's probably not worth getting it repaired as it also seems to have a battery issue (it shuts down immediately when the power cable is disconnected).

Could anyone please advise about how I can recover files from the 2015 Macbook Pro? Any assistance would be greatly appreciated.