Hi!
Do airline pilots and others log P1 time when the autopilot is engaged.
Of course they do. If not, then some 20.000+ hours grey-haired airline veterans would have less than 100 hours in their logbooks (not even enough for their license renewal) ... especially those who fly long-haul.
I have always logged actual IFR only when I actually fly, not manage, the aircraft therefore I know that my IFR time logged is accurate.
Wow! And how do you do that? Start your stopwatch whenever you enter clouds and stop it, when you leave it? That's quite a job on a summer day with Cu clouds everywhere...
All pilots and instructors that I have ever encountered have logged as IFR time those flying hours that were flown with an IFR clearance. Because these are also recorded and documented with the relative ATC units in case of any doubt.
Greetings, Max