No it doesn’t! The hosted plans are not licenses to use any part of Discourse, they are simply hosting plans. Plugins are split between plans to allow a more efficient setup, as more plugins require more computing resource (RAM, storage, CPU speed etc). So you can use any plugin and as many plugins as you like on a self-hosted instance while taking note of the needed computing resource.
If you need a way/guide to setup OpenID with Amazon Cognito, see this guide here: Anyone have a working AWS Cognito configuration w/ ouath2, openid or sso? - #4 by weallwegot
Feel free to always use the search 
to find stuff like this 
, I just found that by searching.