Selfhosted

Sure :)

I knew about bit rot but thought the only solution was something like a zfs pool.

Right. There are other ways of doing this but a checksumming filesystem such as ZFS, btrfs (or bcachefs if you're feeling adventurous) are the best way to do that generically and can also be used in combination with other methods.

What you generally need in order to detect corruption on ab abstract level is some sort of "integrity record" which can determine whether some set of data is in an expected state or an unexpected state. The difficulty here is to keep that record up to date with the actually expected changes to the data.
The filesystem sits at a very good place to implement this because it handles all such "expected changes" as executing those on behalf of the running processes is its purpose.

Filesystems like ZFS and btrfs implement this integrity record in the form of hashes of smaller portions of each file's data ("extents"). The hash for each extent is stored in the filesystem metadata. When any part of a file is read, the extents that make up that part of the file are each hashed and the results are compared with the hashes stored in the metadata. If the hash is the same, all is good and the read succeeds but if it doesn't match, the read fails and the application reading that portion of the file gets an IO error that it needs to handle.

Note how there was never any second disk involved in this. You can do all of this on a single disk.

Now to your next question:

How do I go about manually detecting bit rot?

In order to detect whether any given file is corrupted, you simply read back that file's content. If you get an error due to a hash mismatch, it's bad, if you don't, it's good. It's quite simple really.

You can then simply expand that process to all the files in your filesystem to see whether any of them have gotten corrupted. You could do this manually by just reading every file in your filesystem once and reporting errors but those filesystems usually provide a ready-made tool for that with tighter integrations in the filesystem code. The conventional name for this process is to "scrub".

How do I go about manually detecting bit rot? Assuming I had perfect backups to replace the rotted files.

You let the filesystem-specific scrub run and it will report every file that contains corrupted data.

Now that you know which files are corrupted, you simply replace those files from your backup.

Done; no more corrupted files.

Is a zfs pool really that inefficient space wise?

Not a ZFS pool per-se but redundant RAID in general. And by "incredibly costly" I mean costly for the purpose of immediately restoring data rather than doing it manually.

There actually are use-cases for automatic immediate repair but, in a home lab setting, it's usually totally acceptable for e.g. a service to be down for a few hours until you e.g. get back from work to restore some file from backup.

It should also be noted that corruption is exceedingly rare. You will encounter it at some point which is why you should protect yourself against it but it's not like this will happen every few months; this will happen closer to on the order of every few decades.

To answer your original question directly: No, ZFS pools themselves are not inefficient as they can also be used on a single disk or in a non-redundant striping manner (similar to RAID0). They're just the abstraction layer at which you have the choice of whether to make use of redundancy or not and it's redundancy that can be wasteful depending on your purpose.

I was thinking whether I should elaborate on this when I wrote the previous reply.

At the scale of most home users (~dozens of TiBs), corruption is actually quite unlikely to happen. It'll happen maybe a handful of times in your lifetime if you're unlucky.

Disk failure is actually also not all that likely (maybe once every decade or so, maybe) but still quite a bit more likely than corruption.

Just because it's rare doesn't mean it never happens or that you shouldn't protect yourself against it though. You don't want to be caught with your pants down when it does actually happen.

My primary point is however that backups are sufficient to protect against this hazard and also protect you against quite a few other hazards. There are many other such hazards and a hard drive failing isn't even the most likely among them (that'd be user error).
If you care about data security first and foremost, you should therefore prioritise more backups over downtime mitigation technologies such as RAID.

RAID 1 can absolutely be faster than a single disk for read perf, and on Linux it is tuned to be faster.

You're missing the point entirely. I never said to use a single disk, I explicitly compared it to RAID0.

As far as data security is concerned, JBOD/linear combination and RAID0 are the same, so you'd obviously use RAID0 if you didn't need redundancy.

if it’s a 1:1 full disk image, then there’s almost no difference with the costs of raid1

The problem with that statement is that you're likening a redundant but dependant copy to a backup which is a redundant independent copy. RAID is not a backup.

As an easy example to illustrate this point: if you delete all of your files, they will still be present in a backup while RAID will happily delete the data on all drives at the same time.

Additionally, backup tools such as restic offer compression and deduplication which saves quite a bit of space; allowing you to store multiple revisions of your data while requiring less space than the original data in most cases.

In this case he’s talking about restic, which can restore data but very hard to do a full bootable linux system - stuff needs to be reinstalled

It's totally possible to make a backup of the root filesystem tree and restore a full system from that if you know what you're doing. It's not even that hard: Format disks, extract backup, adjust fstab, reinstall bootloader, kernels and initrd into the boot/ESP partition(s).

There's also the wasteful but dead simple method to backing up your whole system with all its configuration which is full-disk backups. The only thing this will not back up are EFI vars but those are easy to simply set again or would just remain set as long as you don't switch motherboards.

I'm used to Borgbackup which fulfils a very similar purpose to restic, so I didn't know this but restic doesn't appear to have first-class support for backing up whole block devices but it appears this can be made to work too: https://github.com/restic/restic/issues/949

I must admit that I also didn't think of this as a huge issue because declarative system configuration is a thing. If you're used to it, you have a very different view on the importance of system configuration state.
If my server died, it'd be a few minutes of setting up the disk format and then waiting for a ~3.5GiB download after which everything would work exactly as it did before modulo user data. (The disk format step could also be automatic but I didn't bother implementing that yet because of https://xkcd.com/1205/.)

ZFS and BTRFS' integrity checks are entirely independent of whether you have redundancy or not. You don't need any sort of RAID to get that; it also works on a single disk.
The only thing that redundancy provides you here is immediate automatic repair if corruption is found. I've written about why that isn't as great as it sounds in another reply already.

Most other software RAID can not and does not protect integrity. It couldn't; there's no hashing. Data verification is extremely annoying to implement on the block level and has massive performance gotchas, so you wouldn't want that even if you could have it.