Not sure what exactly you mean with "open source OS" and if Lineage counts as one in your book: it supports quite a few cheap and also fairly recent Motorola phones, which are also easy to unlock:

https://wiki.lineageos.org/devices/#motorola

For family, I just got a used Edge 30 Neo for ~100$ and put LineageOS on it, and it works like a charm. Phones like the Moto g84 go for even less and still can be bought new for a decent price.

Xiaomi would be even cheaper, but I would highly discourage getting one because the unlock process is plain ridiculous nowadays.

And as others have already noted, if you don't mind getting a phone that's a few years old, a used Pixel 5 is not expensive (still happily using a Pixel 4a and don't see why I would need to upgrade).