Does an open position count against the limits?
Yes, in both directions. An open loser can breach you before you close it, and an open winner permanently raises your floor.
Both floors are measured against equity, and equity includes whatever is floating on an open position. Nothing has to be realised for the account to be gone.
The half that surprises people is the other one. Your peak equity counts open profit too, so a rally you never banked raises the trailing floor and keeps it there. Run a position twenty points into profit, give it all back, and you have moved the floor up under yourself without a single closed trade to show for it.
The floors are read at the deepest your equity went, not where it settled. A trade that went through the floor at 14:52 does not survive by finishing green at 15:10.
This is the single biggest difference between a prop account and a brokerage account, and it is why a strategy with a good end of day record can still fail here.