Good practices between SQL and elasticsearch
The most common setup for critical business data is having e.g. a SQL database as your primary datastore and Elasticsearch as additional search index. (= your solution 3).
An alternative for non business-critical data like logs etc. is having Elasticsearch standalone.
Solution 2 seems wired, is not an option for me.
Because you may have a lot of business rules mixed into you database and application using it, I would be conservative and keep the DB. And use ES to index the user attributes I want to search on. ES would return scored results. When a result select I would switch to DB to retrieve all information and relations.
So I would choose 2b : keep DB and store PK in ES, not ID in DB).
Keep in mind you can force the ID en ES. It could be "user_PK" or something alike.