There is an index for ServiceDate on that table, although that table has a ton of indexes on it. We're very likely trying to do too much here (indexes with sensible names = us, the two new ones at the bottom are Azure performance indexes it's added and is validating):
No, I don't think that @CaTs (categories) has many rows. This query is part of a larger that that's attempting to validate new claims against a set of rules of various categories. We're first determining what categories might apply, then finding relevant paid claims that might be relevant in the evaluation.
Yes, absolutely that index exists:
CREATE NONCLUSTERED INDEX [IX_ClaimPaidDetail_ClaimID] ON [Claims].[ClaimPaidDetail]