Symptoms
I used KeepassXC as my system Keychain quite a long time without any problems. Recently I noticed VSCode skipping keyring unlock prompt. Even if KepassXC database is locked, it somehow stores and remembers login credentials. Other applications, like Slack was more than happy to use DB triggering unlock prompts, whenever DB was locked, hinting that KeepassXC and whole Secret Service thing working correctly.
Fix
Go to $HOME/.vscode, find file called argv.json. Open it in any editor and search for this line:
{
"password-store": "basic"
}
Available values are kwallet5, gnome-libsecret, kwallet, basic. Apparently this allows you to inform VSCode about your keychain type, if it fails to detect it for some reason. Remove that line or change value to gnome-libsecret. More info from VSCode documentation located here.