As Rich notes, the Nest Binding does not support Nest speakers and displays. I don’t think the Nest API exposes anything for speakers/displays (but I could be wrong about that).
I’m also not aware of third-party devices being exposed through the Nest API. Note that this could change due to the adoption of Matter, which leads to my next thought.
Google has a habit of changing everything without much warning, and there’s so much uncertainty both with Matter and Google Assistant that I wouldn’t rely on what works today to still work tomorrow. I use a lot of Google products, but I’m never surpised when they blow things up. So even if you could use the Nest API, you’d have to accept that it may lead to wasted effort and extreme frustration.
I think this is probably overwhelming to you right now, so I get why you’d want a list you can search. Unfortunately, it’s basically impossible to keep such a list up to date, and an outdated list can be even more frustrating than no list at all. Let’s try to make it a little simpler.
We usually suggest that newcomers start by searching the community for devices you’re interested in (e.g. locks, light switches, sensors) and then asking if you don’t find anything. You’ll find that we’re quick to jump in with suggestions based on current knowledge. We just like people to search first, because many questions have already been answered.
If you want to stick with WiFi, then I personally recommend TP-Link Kasa devices for ease of use and affordability. You’ll also see discussions about Tuya devices, which you’ll often find on Amazon using random brand names. If a product listing says that the device works with the “Smart Life” or “Tuya” apps over WiFi, then there’s a good chance it’ll work with the unofficial SmarthomeJ Tuya binding. “Unofficial” means that you have to add it to openHAB manually, but that’s super easy.
Some Tuya devices can be flashed with an open-source firmware called Tasmota, but that’s not always the case.
Others recommend Sonoff WiFi devices, which can also be flashed with Tasmota or used with a binding that’s still in development. I don’t have personal experience with these devices.
Many of us use Z-Wave/Zigbee for battery-powered sensors (temperature, door/window, water leak, etc.), because they’re low-power devices (WiFi is not). These can be a little trickier to set up, but there’s lots of past discussion about them and lots of help available.