I would check the directories using ssh, and also check out in which group(s) the account is present.
The synology interface is a limited version of the underlying linux permissions, which doesn’t tell the entire story.
I’m not sure how you run sonarr on your syno, but I’m guessing through the synocommunity package? If yes, a change on the synocommunity package has caused many people issues in the (quite recent) past: New sc-download setup can’t access files even with full permissions
That thread has a lot of useful information, but you do need to have some synology and linux knowledge.