We actually wrote another blog about this because I had the same question. I am the CEO of DoltHub so I can have my engineers write stuff to explain it to me :-)
Right now, DoltHub (https://www.dolthub.com/) will still work as a remote but all the SQL there will be the MySQL version. Over time the Doltgres storage format may become more bespoke and we'll have to figure out how DoltHub will work.
Queries on DoltHub need to go to S3 to fetch all the chunks. This only works for databases < 1GB generally. You will get much better performance if you clone the database locally.
https://www.dolthub.com/blog/2025-06-26-prolly-tree-balance/