Hey there! I’m a longtime gamer, and decided that the google doodles was a nice beginning into speedrunning.

Is there a discord server for the running of google doodles?

Yep! https://discord.com/invite/7MXyJHs

You can also find certain Discord servers for certain doodles, such as the Google Doodle Champion Island Games Begin! Discord. In order to find a Discord server on speedrun.com for a certain game, look under the "Follow" button for the Discord icon.