Fiction distorts reality
Catherine's Gothic reading gives her a script for the world that keeps failing her. Austen shows how the stories we consume shape what we expect to see, and how those expectations can make us blind to what's actually happening.
Social performance vs. sincerity
Almost every character in Bath is performing. Isabella performs friendship. John Thorpe performs confidence. General Tilney performs respectability. Catherine's honesty makes her an outsider in this world, and also the character the reader trusts most.
Education through embarrassment
Catherine doesn't learn from lectures. She learns from getting things wrong and feeling the sting of it. Henry's correction at the Abbey and the General's expulsion both teach her things no drawing-room conversation could.
Class and money as social weapons
General Tilney's treatment of Catherine is entirely driven by his belief about her wealth. When that belief changes, so does his behavior. Austen shows how money determines social worth in ways that have nothing to do with character.
The gap between Gothic fantasy and English reality
The novel keeps setting up Gothic expectations and then deflating them. The mysterious chest holds laundry. The locked cabinet holds old receipts. Austen uses that deflation to argue that real life has its own dangers, and they're less dramatic but more common.