manord

Caveat - I've never used the MAN T3 airside connection myself. However, I use BA & AA in/out of MAN T3 fairly often.

Your connection should be comfortable. You might be the only person, or maybe just a handful, making a domestic-international connection, so very unlikely to be any queues. There will be a biometrics check, but not security (I think). You'll probably have time for a lounge visit (QF gold travelling on AA gets you into the BA lounge at T3).

Even if you have to go landside and back through security again, you still should have time, although you might need some brisk walking if you want to be sure of being at the gate before boarding starts, due to the normal AA gates being at the far end of the terminal.

The catches I see are:
(i) the relatively common risk of delayed LHR-MAN flights. But then it becomes BA's problem to get you to your destination, so should be fine. Although you might want to look at the impacts on the rest of that itinerary.

(ii) you might discover the airside connection is closed due to lack of expected users at that time (but see comment about going landside above).

(iii) the risk of missing the airside connection route. The signs and route could be easy to miss depending on which gate you arrive at. I've found the most common arrival gate for BA LHR-MAN recently to be gate 142/143/144. As you leave the jetbridge, you will go down a set of stairs. The signs are in the corridor you enter at the bottom of the stairs and might require you to look backwards (rightwards) against the flow of passengers to see the signs.

Short answer, given the flexibility you mention "worst case, next day is OK" then I'd be very comfortable booking this.