IMO Brighton took foot off the pedal second half which is why you had half a chance. They were happy to sit back and onus was on you to make something happen. The damage had been done though, and I never thought you'd get back into it. But of course, I was rooting for Brighton.
We are also in "transition" then as we are also hung over from replacing our long-term manager. We are not as far along in the process as United though - SAF retired 5 years before Wenger.
Arteta is coming up to 3 years with us, though he came halfway through 19/20 season. In that time, he's won the FA Cup and finished 8th twice (including when he came in mid-way through season) and 5th, and got to SF in EL. I suppose how much of a failure or success he has been so far depends on your expectations. I know most people probably feel that City are on another level and everyone else is really just competing for top 4. I have been "Arteta out" for most of that time. Needless to say I feel quite differently atm. One thing I will say is that this team is Arteta's through and through now; only Xhaka precedes him at the club. So far, it looks like the faith the board has placed on him is justified. It started to come together last season (pity about our typical collapse at the end), and that progress looks to be continuing (tough squad depth is still not there).
As for United, you've had 3 managers since SAF (Solskjaer, Mourinho and LVG) who were in charge for about 2 years (you say the process takes about 1 season). Does that mean you've had about 3 transition periods? Anyway, I guess my point is it's a bit of a vague and meaningless term and like I say, United seems to have been in transition for almost a decade.