Hey @kazag,
let me give you a quick (but not final) answer instead of the assigned personnel.
It is currently not possible to simply add ESLint rules to SonarLint itself, only when using in connected mode with SonarQube or SonarCloud as the rules are loaded via the connection.
I am not aware of the scope of the SonarJS analyzer and if it has a 1-1 replacement of ESLint rules, based on your answer I might forward this topic to the specific analyzer developers.
I’ve seen the option to use ESLint results in your CI build (e.g. THIS article) but in order to fulfill your third option you require something else. The issue is, for SonarCloud there is no possibility yet to add custom rules.
If you decide at one point to switch to SonarQube, there is the possibility to add coding rules. Maybe there is a community plugin with ESLint, but that is out of my scope or you want to write one on your own.
Again, feel free to answer if something is not clear or you have an idea and we can provide you with information on the feasibility.
Best,
Tobias