Yes, they do. Check
eero's release notes. For example, they introduced 802.11k and 802.11v support in October, 2021. They started supporting 802.11r in June, 2017.
No single vendor controls wireless clients. You have to support at least 802.11r if you want wireless clients to hop from radio to radio more quickly. (802.11k and 802.11v are less important, and some clients don't support those protocols.)
The OpenWrt community consensus is that 802.11r is the most important protocol for roaming, and I think I agree with that. I've never seen 802.11k/v supported without 802.11r, but maybe I haven't looked hard enough.
802.11s is an attempt to get some multi-vendor standardization, but it doesn't seem to have caught on.
That's really a different thing, albeit related. You can have a wireless network with 802.11r/k/v — with some protocol such as 802.11s providing coordination between access points — and still manually tweak aspects of your network (channel widths, transmission power outputs, channel selections including possible DFS channel rescans and resets, etc.) I do that, actually.
Eero devices specifically won't let you do that. They try to optimize for the local environment automatically and don't include many manual overrides.
Yes, absolutely. With wired backhauls if at all possible. (Use MoCA 2.5 adapters if you have coax ports and don't want to run new wires.)
I suppose a notable exception is OpenWrt. That is, it's the firmware that matters, not the actual manufacturer of the device itself. And I suppose MikroTik's RouterOS is another exception since it can run on some non-MikroTik equipment such as a mini PC.
