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I accidentally installed a windows installation media to my harddisk which contained 10 years worth of documents and files, which formatted the drive and deleted all the files. I was able to recover almost 1 TB data using photorec but it's impossible for me to rearrange and rename even at least the essential documents I can. I ran testdisk and in the analysis I found the part of the partition that went RAW. When I try to list the files it says filesystem damaged.



My questions are

Should I proceed with write? What would write do in this case? Would it save my files with their last directories and names? If not, which programs would help me recover the data with directories and names intact?

Thanks!

There is no "write" function on this screen!

You would select each partition found and try to run "list files" with the p-key.
If you discover missing content inside you have the option to copy files and folders to another location (select another drive!).
If that feels you can run deep search and repeat the procedure above.

When running write after deep search, Testdisk would write the partition table again according to its findings including your latest modifications.

I have not software I can recommend.
Typically the recovery software offers you modes of free testing so that you can compare them all.