The extension is not in the Chrome Web Store yet. You load it from a folder on your disk, once, and Chrome keeps it. Chrome 123 or newer.
download the newest testomat-io-<version>.zip from
Releases —
the single file under Assets — and unpack it, or

git clone https://github.com/testomatio/browser-extension.git
chrome://extensions and switch on Developer mode (top right).Click Load unpacked:

…and pick the folder:
extension/ folder inside it, not the
repository root.Either way, the right folder is the one with manifest.json directly
inside.
Click the puzzle icon in Chrome’s toolbar and pin Testomat.io with the pushpin:

There is nothing to build or install beyond that — the folder runs as is.
There is no auto-update. To get a new version:
git pull in the clone.On chrome://extensions, press the reload (↻) icon on the Testomat.io
card:

Your token, settings and unsent results survive the reload.
chrome://extensions.extension/ folder inside it.chrome://settings/help).