Real Broker agents routinely coach buyers on this before a showing, because your maximum budget is the most damaging thing to reveal. A seller's agent presenting offers only needs to know you will go higher, not what your actual ceiling is, and an overheard number becomes the negotiation's starting point rather than your own opening offer.
A visible deadline, needing to be in before a job start date or a school year, invites a seller to hold firm rather than negotiate, since urgency on your side reads as leverage on theirs, whether or not anyone was actually listening at the door, in a market currently running at 1.63 months of supply.
Keep the real conversation about price, timeline and strategy for your agent, away from the house itself. Get your hand-reviewed valuation from Joel Dyck.