mastodon.social is one of the many independent Mastodon servers you can use to participate in the fediverse.
The original server operated by the Mastodon gGmbH non-profit

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Andrew Escobar (Andres)

Yet another annoyance that follows us around the web: “Sign in with Google”

You can disable these prompts, but Google buried the option:

Manage your Google Account ⇢ Security ⇢ You connections to third-party apps & services (“See all connections”) ⇢ Settings (gear icon) ⇢ Google Account sign-in prompts: OFF