Not so, oh regional person.

On codeshares, the BA flight prefix is irrelevant. You've bought a BE (or BD or EI) product but with a BA price tag on, that's all.

Your BP will have the BE flight number on. If you're lucky, it may state "marketed as BA xxx", but that has about as much relevance as a jam donut to the non-BA ground staff.

Lounge access will be according to BE rules, unless they have any specific agreement with BA to the contrary. Sometimes it's even worse than that - sometimes you don't even get the lounge access provider by the operating carrier, as it's not their ticket.