If BA297 is late, say 30 min, and I fail to make the connection due to this delay, and AA will only rebook me on the next AA flight the following day, I will for sure claim reimbursement of hotel costs and 600 Euro compensation from BA for delay.

Under EU Reg. 261/04 it is not required that BA297 is 4 hours late; any delay of this flight leading to arriving > 4 hours late at final destination (because e.g. missing the last connecting flight of the day) means that compensation is payable - unless the delay of BA297 is caused by "extraordinary circumstances". It will only make it worse for BA, if AA refuses to rebook on the last flight of the day (the UA flight) and this will expose BA to liability for delay under EU Reg. 261/04.