Can we reconstruct/reset a broken Postgresql data directory without losing data?
It may be possible to rescue some of your data. It will not be straightforward.

Hopefully you took a full file-level backup of your postgres directories as soon as you noticed the problem. A recent filesystem backup will also he useful.

Then, subscribe to the postgresql-general mailing list and post a full description of your problem there. Bear in mind it is the weekend and you will need to be patient.