An official announcement regarding Stadia was posted a few days ago. ESO standard edition will be available with a Stadia Pro membership and Stadia players will be crossing playing on the PC/Mac megaservers. What about your existing character progression and purchases?
Thanks to Stadia’s PC crossplay and cross-progression support, you can pick up and continue your adventures if you previously played ESO on PC/Mac or Steam, meaning you won’t lose any progression and be able to access all your characters and continue playing with your friends and guildmates as normal on the PC NA or EU megaservers. You can even switch playing between all PC platforms (PC/Mac, Stadia, Steam) at will.ElderScrollsOnline.com
I’ve noticed that ESO has updated the account areas of the website to include Stadia logins. Based on all this information, I believe that you will be able to link your existing ESO accounts to Stadia and have access to all your existing content (DLCs, crowns, etc.). However, I suspect you will need purchase the Stadia Pro membership or the base game on stadia in order to play ESO.