I personally think he benefitted from Barca coming to the end of their cycle rather than him having solved Barca as a problem.
That’s not to say his low block wasn’t effective to a large degree but the Inter side did it in a more stylish way and their first leg win was tactically outstanding.
For me it was a turning point as post that era with Madrid, he was good but he was never a Champions League threat ever again. So it does mark the beginning of his downfall as an elite elite manager. His level dropped since then albeit still has won league titles.
You can say that of his third year in Real, not the first.
He joined Real with Barça that in the previous 2 years only lost 2 titles: a copa del rey to Seville (irrelevant) and the CL to Mourinho itself. And Barça ended up winning the league and CL again with Mou in Real.
It was nowhere in the end of their cycle.
His first games vs Barça were atrocious, but that is kinda "normal" when you have one of the best teams of all time vs a team that were in process of massive change in style.
After that he won a token copa del rey in his first year and went on to win the league (best ever league performance in Spain) and lose the CL semis on penalties. This is no downfall at all and people were expecting Real to continue to be ruthless.
They imploded instead and this is when people lost faith in him - based mostly on a weird public perception of him as finished (he had been champion the year before and lost again in the CL semis, being 2nd in la liga). Barça meanwhile was good enough to win the league with the manager absent for half the season.
After Real Mourinho didn't get any job that was simple and with expectation of easy league titles: Chelsea, Man Utd, Tottenham, none of them were expected to win the title easily.
He was champion with Chelsea then another abrupt unexpected fallout made his 3rd season collapse. Man Utd was a team fighting for top 4 and still is (let's see if this year they can keep challenging for the title) while Tottenham is a team almost winning but without any title since 2008.
So his widely announced downfall is kinda relative given the state of the teams he has managed since.