I want to use the Chromium source to build a stable browser version. But I do not understand how to determine stable chromium source versions because it is released several times to day, and releases have no stable or intermediate marks. By stable version, I mean the version that is tested by some QA group and is marked as ready for production.
The daily builds that you are referring to are canary builds which are for development purposes only. If you want to check out a stable build from the Chromium repo then you need to find out the stable version.
For that you can go to https://omahaproxy.appspot.com/ and find out the current/previous stable version of Chromium/Chrome. Use channel and current_version columns as a reference.
Chromium uses tags to represent a specific version. So, for example, if the current stable version is 89.0.4389.90, execute the following git commands from your Chromium repo:
Fetch the remote tags:
git fetch --tags
List all the available tags (Optional):
git tag
Checkout the specified tag:
git checkout tags/89.0.4389.90
After checking out a specific tag, follow the commands here to pull third-party deps here