The first step of Visual Studio Code install is deceptively simple: download the .deb file, double-click to open.

Trying to log into accounts causes a notification/error:

You’re running in a GNOME environment but the OS keyring is not available for encryption. Ensure you have gnome-keyring or another libsecret compatible implementation installed and running.

The keyring troubleshooting page provides some clues but it’s a bit clumsy to figure it out.

1. Problem 1: libsecret is not installed on a fresh Linux Mint v22.3.
   Solution: install with apt install libsecret-1-0 libsecret-1-dev libsecret-tools (not sure all of them are required).
2. A bit buried in the docs is this bit: “and ensure the default keyring (usually referred to as Login keyring) is unlocked”.
   Problem 2: there was no “Login” password keyring visible in Seahorse (the keyring manager).
   Solution: First, it’s very possible a restart (of gnome-keyring) after installing libsecret might have auto-fixed this issue, but I went ahead to try to create that and failed: the UI was not showing the new keyring, so restart was in the cards anyway.
   After restarting the computer, I was able to create the new Login password keyring and Visual Studio Code worked without any issues. It didn’t even require the --password-store="gnome-keyring" argument or startup setting.

Also thanks to this SO answer and this one too.