After the work by @onsummer in #11080, this plugin could be a good way to ensure consistency going forward.

The default rules might require too much change at once. We could phase the implementation as follows:

First PR

1. Add the dependency
2. Update .eslintrc.json and .eslintrc.json
3. Enable the check-types rule only, setting it to "error"
4. Confirm that the results match what we implemented in Use primitive type instead of constructor type #11080

Later PRs

Test more of the recommended rules, and enable the ones that give the best return on effort. We could prioritize as follows:

1. Rules that don't require much change to our docs. These will enforce existing doc style going forward
2. Rules that flag behavior that can be auto-corrected with the --fix option. For example, check-tag-names to replace @return with @returns
3. Rules that flag serious errors like invalid tag names