It's weird now. You used to have to go through passports in the same line as all Americans and have your brp card and fingerprints checked. Airports in UK now operate with e-gates, so Americans go through them like UK and EU citizens do.
It's been a common topic of conversation on here for awhile as you don't get a stamp when you use e-gates. The experts have reassured everyone on here that everything can be checked electronically now so not to worry about no stamps for re-entry (still needed for newbies with initial entry). Which is what the airline attendants said to me every time I asked where to go with my card.
I have to admit, it still makes me nervous, but I'm trying to calm myself as many people have had no problem with it when submitting citizenship applications.
If in doubt, ask an attendant if you are unsure. Just remember to still take your BRP card with you just in case. My first time through the e-gates was at 1am and apparently my face was not recognisable and I was sent to a person lol