Same problem and I totally agree with many of the earlier posts that this is absolutely ridiculous.
I couldn't be sure I had backups of my data so getting the data off the drive is paramount for my situation.
Anyway, two possible solutions for you guys to try:
1) Connect to another computer and start the effected computer in Target mode (so the problem computer shows up just as a hard drive). Then transfer any pertinent data off the problem drive.
*this didn't work for my situation as my problem 2012 MBP has Thunderbolt 2 and my 2017 iMac is thunderbolt 3. Two frustrating trips to the store and back and...
2) Connect an external HD or thumb drive (I had an old 500GB HDD laying around). Restart in recovery mode. Install Mac OS Mojave on this drive. Once it's done it will show the full (ish) internal drive. Transfer data off the problem drive.
Then install Mac OS Mojave on the internal drive via a recent time machine backup as mentioned in earlier posts. This way the TM backup could be a little old and I don't care. Data is safe, MBP is running a stable OS again.
I'll be staying away from Catalina for a long while. Very not happy about this problem.
Grateful you guys took the time to post.