Linux

I have a lot of tar and disk image backups, as well as raw photos, that I want to squeeze onto a hard drive for long term offline archival, but I want to make the most of the drive's capacity so I want to compress them at the highest ratio supported by standard tools. I've zeroed out the free space in my disk images so I can save the entire image while only having it take up as much space as there are actual files on them, and raw images in my experience can have their size reduced by a third or even half with max compression (and I would assume it's lossless since file level compression can regenerate the original file in its entirety?)

I've heard horror stories of compressed files being made completely unextractable by a single corrupted bit but I don't know how much a risk that still is in 2025, though since I plan to leave the hard drive unplugged for long periods, I want the best chance of recovery if something does go wrong.

I also want the files to be extractable with just the Linux/Unix standard binutils since this is my disaster recovery plan and I want to be able to work with it through a Linux live image without installing any extra packages when my server dies, hence I'm only looking at gz, xz, or bz2.

So out of the three, which is generally considered more stable and corruption resistant when the compression ratio is turned all the way up? Do any of them have the ability to recover from a bit flip or at the very least detect with certainty whether the data is corrupted or not when extracting? Additionally, should I be generating separate checksum files for the original data or do the compressed formats include checksumming themselves?