Support repairing Persistent Storage filesystem

... when it can't be automatically repaired by e2fsck -f -p.

Closes #15451 (closed), #20498 (closed)

Note that parts of this merge request have been merged out-of-Gitlab: 5b6303ca . This happened to bring the code in stable, so that we have more chances to discover bugs. But some threads were still open, so we're keeping the MR open. This explains b91a5ae4