what linux OS should I install on a backup notebook if my main one is debian?

It depends:

• If your backup notebook will only rarely be used, then just make it Debian as well. I can't think of a reason why you'd make it harder on yourself for those spare times you'd have to rely on the backup notebook. (As a side note, if your main system was on a rolling release (like e.g. Arch), then there would be merit in going for a different (i.e. more stable^[1]^) distro (like e.g. Debian Stable) on the rarely used backup. This is tied to the fact that rolling release distros somewhat require you to update every so often for proper functioning. This hassle is simply absent on distros like Debian Stable etc.)
• However, if the backup notebook will be used as a second system of sorts for all kinds of needs and does not have to be reliable per say, then please be my guest and quench your distrohopping thirst to your hearts content.

Install linux mint, so I get ubuntu but without them throwing their subscription services down my throat.

Linux Mint does indeed provide you some Ubuntu goodies without its associated negatives. But, perhaps it's worth mentioning LMDE; i.e. Linux Mint Debian Edition.

I’m unsure about other advantages

Linux Mint does a lot of heavy lifting to provide a seamless and polished experience. This does come with being more opinionated than either Debian or Ubuntu is. However, one might argue that they're just offering the bare minimum that your average Linux user would want on their systems anyway. Hence, it's unsurprising that Linux Mint has become the go-to distro for many newbie and veteran Linux users alike. You don't know what you're missing if you're unsure of other advantages...

maybe the more frequent program updates? Kernels are also updated more often than with debian as far as I know.

FWIW, Debian also has its testing and unstable releases.

Do you know of other advantages?

As has been previously alluded, Debian is pretty bare-bones compared to Linux Mint. So, if you're mostly interested in setting up things exactly as you'd want to, then you should go for Debian and build it up as you go. However, if you're more in favor of sane and opinionated (albeit bloated to some) defaults, then Linux Mint takes the cake. Ultimately, you'd have to experience it for yourself and come to your own conclusions.

Go for FreeBSD

😅

this might require a learning curve, because this is an OS I’ve never used.

Yup.

Are commands that different from debian?

Debian (and its commands) are more similar to Arch, Fedora or any Linux distro for that matter than it is to FreeBSD. Like, it's a pretty significant departure. And one, I'd argue, you're simply not equipped for (yet).

Overall, I think making the move to FreeBSD doesn't seem like the logical next move for ya. Its ecosystem (unfortunately) is a lot less developed compared to Linux. And while there are definitely some pros and cons to it, I just can't fathom why your average user would use it without properly knowing what they're getting into and why they're deliberately and consciously making that choice. If you allow me, may I ask you where this interest to FreeBSD stems from?

other more niche linux OSs seem too much a hassle and I guess won’t be as supported as the main ones.

Do Arch, Fedora or openSUSE (to name a few) fall under "other more niche linux OSs"? Furthermore, do you think that FreeBSD will be less of a hassle compared to "other more niche linux OSs"?

1. The term "stable" is used here to mean slow cadence of change which manifests most commonly as little to no updates in-between point releases. These point-releases occur annually/biennially and come with big updates/changes. As you might expect, a distro with a release cycle as such comes with the added benefit that (little to) no breakage should occur until the next point release. Hence, these distros are (rightfully) associated with providing reliable and robust experiences. Though, this does not mean that they have a monopoly on this. When used responsibly, all (if not most) mainstream/popular distros are able to provide reliability and robustness.--