Nest 1st gen and 2nd gen thermostats no longer supported from Oct 25

What are the best ways of finding such devices? Almost all the time when I look into some product it ends up being connected to some random cloud service with its own login.

It isn't easy, but you just have to do your due diligence and really explore the featuresets available for a given category of product.

A shortcut however is checking out the homelab subreddit. People will post about the gear they are using in their stack.

HomeAssistant supports a bunch of home automation systems, including local-only ones like ZWave and Zigbee*. A search for "zwave thermostat" comes up with a lot of results, though I couldn't say how difficult it might be to configure them (I'm only using simpler devices like switches and sensors).

* There are internet-connected controllers and local controllers so you'd also want a local controller. I've used an Aeotec Z-Stick for ZWave devices for around a decade, it plugs into USB, HomeAssistant accesses it directly, and the ZWave network itself is connections between the Z-Stick and the devices without the internet.

The Honeywell Z-Wave thermostats are trivial to connect and work with via Home Assistant.

Source: I own one. :)

I own two and they are bulletproof with Home Assistant. When away from home I just wireguard in and adjust/monitor as needed.

One way is to look for devices that have unofficial firmware available, so you can just overwrite the included software for something more under your control. For example, check out Tasmota, "an open source firmware for Espressif ESP8266, ESP32, ESP32-S or ESP32-C3 chipset based devices": https://tasmota.github.io/docs/