I've had really good luck with the one generation old relatively up-market Dells - their consumer products tend to be mediocre, but the Latitudes and Precisions are typically good hardware ... look for Dells that start with a "7".
My little 12-13" class carryin' around laptops for the last many years have been a first-party refurbished Latitude E7250 succeeded by a similarly refurb Latitude 7390. Replacement after not quite 5 years because I finally got a tiny hairline crack in the LCD that caused some discoloration in the corner of the screen, from a hit that would have bent the corner of an aluminum chassis machine, and it was starting to struggle with running video conferencing at the same time as my usual workloads. First party refurb meaning https://www.dellrefurbished.com/ - It's a joint venture by FedEx and Dell, stock is "whatever they have right now" but there are always machines coming through, and there are usually coupons that make it even cheaper, so pick what you want and watch for a few weeks if you can.
As you note, going for a generation old machine not only gives time for the hardware support to settle out, it makes it _much_ cheaper: Both of those were around $500 for examples optioned up to 1920x1080 screens, the newer one has 16GB of RAM in it, etc., and I kind of prefer that the machine I carry around day-to-day isn't something I have to be super precious about.
In the two example cases, everything _except_ a Broadcom smartcard reader that I don't have any compelling use for anyway worked out of the box with little-to-no configuration, I get credibly 10-12 hours of usable battery out of the newer one (I'm running a full-integration KDE on Arch setup, so it's not light but it's also running active power management), and the 7250's (readily replaceable if I chose to) battery still has 78% of its design capacity after years of cycles.
...or if you want a truly low-end beater, buy an EOL Chromebook for like $50, flash a UEFI Coreboot payload (MrChromebox maintains builds for most of the common models) and hack on it mercilessly. They're low-end, but are fine at being low end, and the ones built for the education market will take a _beating_. I have one that I use as a media player/reference materials display when doing potentially destructive things like sanding/filing/paint stripping or what have you. I got it to do that as a Chromebook, but after it was getting concerningly out of date once the model passed AUE, I flashed it and now it's usually running some weird stack (currently Hyprland) that I want to try out on a machine I actually use without interfering with machines I do real work on.