[Samsung Galaxy Watch 4] kirvedx:
I tried installing every version from the newest backwards from apkmirror.

The first version to actually work, not only to receive microphone input, but to also provide search results without any modifications or additional apps, is:

Google Assistant Go v2.8.0346747673

If you're wondering how to avoid any third party apps at all and to just install this directly using official tools - it's pretty simple. Follow the Google provided instructions for installing Android Studio and getting binary tools setup in the path for your OS (i.e.):

Download Android Studio for Debian/Ubuntu (or your OS)

Install the downloaded platform

Extract the archive

sudo cp <extracted/root/folder> /opt/android-studio

sudo chown -R user:user /opt/android-studio

nano ~/.bashrc

Then add at the bottom: export PATH=$PATH:/opt/android-studio/bin

Then add below that (this is ADB): export PATH=$PATH: ~/Android/Sdk/platform-tools

Press CTRL+O, then press Y, then press Enter, then press CTRL+X

source ~/.bashrc

If needed, install "Menu Editor" from the app store (menu editor), or

sudo apt-get update && sudo apt-get upgrade && sudo apt-get install gnome-menus

Create using Menu Editor a launcher, that leverages /opt/android-studio/bin/studio.sh as the command for launching Android Studio, with a working directory of /home/<your-user-name>

Launch Android Studio, if it's your first time you'll get prompted to download a system image using sdk manager, so download the latest image (to get the latest platform tools, etc). If you've already got android studio, I'd recommend the latest for the best support - but you probably know what you're doing, right?

Now you're ready to do this like a pro

From here it's pretty darn simple.

Open a terminal

Go to my first link, download that version of Google Assistant Go from apkmirror.

Create a folder in your ~/.Downloads directory named android-apps, cut and paste the file into it

Rename the file to "Google Assistant Go_0.2.8.0346747673"

Do this, so that its easier, but distinct enough that later variants and such can be discernable to you.

Open your watch interface, and:

Swipe from top

Click on the gear (settings) icon

Scroll down to About watch

Scroll down to Software

Scroll until Software version is in sight

Tap on Software version until you've unlocked developer options (You'll get an on-screen notification)

Swipe from left

twice

Scroll up to Developer options

Enable ADB Debugging

Enable Debugging over Wi-Fi (if its ever "unavailable", turn it off, and back on, when connected to Wi-Fi)

Take note of the IP Address (IPV4 minus the port, so the format as follows, excluding the colon and 4 numbers after): 192.168.82.166

Switch over to terminal and perform the following commands (replacing the IP with your IP, and the downloaded renamed APK to that which you named it, obviously):

cd ~/Downloads/android-apps
adb connect 192.168.82.166
adb install "Google Assistant Go_2.8.0.346747673.apk"

Now, open the app (Swipe from bottom, scroll to bottom, tap the icon). Notice it takes a second the first time - but it will be much snappier after it caches and indexes. To remove the blue box and notice at the bottom, go back into terminal:

adb shell wm density 180

Go back into Google Assistant and tap that blue box on the bottom right...you still won't see the whole thing because reducing pixel density will still not change the placement, but this density will allow you to click it (you were able to click it before, it was after doing so that was the problem).

In the next screen, now you can see the tiny little blue button on the bottom right that you couldnt see before...sorta. You can click the arrow to the right of the text in the center if you want. You can even click on it to let it open the Terms of Service on your phone. To get rid of it....touch near that little blue button on the bottom right of your watch, and you'll be returned to the nice and clean main screen of Google Assistant.

Back in terminal:

adb shell wm density reset

Congratulations, you've sideloaded like a pro! Next time? Well obviuosly you're already set up, so it won't be nearly as hard - and you won't have to trust third party app developers or any of the spam, deceipt, or other malicous things that can come if you trust an app designed for one thing at one time and don't ensure it's kept up to date, etc...

Back in terminal:

adb disconnect

Oh, did you want to replace the default app on the side button? To do it legitimately you'll need to wait until Samsung gets their version of GA released, and adds the proper menu to do it, like they did with Google Pay. To do it the modified way, you'll need to sideload GW4Remap (its in this thread), go into Accessibility (from the settings menu), enable GW4Remap, then go into GW4Remap, and remap the side button to GA.

Pretty sweet for now - just wanted to help organize the most guaranteed and forever working way to sideload so that nobody has to trust a third party app to do the process, and confirm my own findings on which version was working.

Thank all of you for providing what information I'm clearly working off of - happy to finally have GA on a Samsung device!