I would temper this slightly by observing that the animosity towards us started when we began to dominate - pretty much from the start of the Pep era. From memory, when we won the league with the Aguero moment, there was great euphoria from media. The hatred ramped up after the Der Speigel leaks.
Any other team might become the victim of jealousy if they start to dominate, or if they threaten to remove one of the establishment clubs. Newcastle have already had their ambitions reined in.
Oh, it certainly got worse under the Pep era and yes dominating will breed resentment for any club is not part of the red cartel to some extent. We are talking about the mainstream media coverage here though at the core and that sort of negative coverage started way before the Pep era for City. The first PL title win broke viewing records and broke up United's dominance(stopped them doing yet another threepeat, when you think about it). They were happy with that but it quickly changed soon after. Also, lets not forget the season before that, was the overhead shin from Rooney, where City were treated with all sorts of contempt, labeled mercinaries, belittled, mocked. They were already in the habit of shitting on all of our signings before they'd even kicked a ball for us(Yaya, Silva etc). This all fits with the theory about United perhaps being the biggest reason for the difference in coverage, with clubs that should in theory be getting the same sort of press treatment. After the first PL win, they desperately wanted City to be the new Blackburn. In fact, those comparisons were frequent in the papers, as I remember it. They seemed happy United won it, as they felt business had returned to normal. Even during that season, there were signs of them worring that it wasn't a one off, given they'd heard Fergie was thinking of retiring. When City had the audacity to deny Liverpool a title the season after, the anti-City machine had gone up a gear. I seem to recall net spend lists started appearing. Then came the 2014 FFP sancations and so on(sweeping Liverpools under the rug).
I guess my point is, you'll find articles with some of the same arguments and complaints for these similar clubs/ownerships(I dug up an article about Chelsea's wage bill ruining football a while back for example) but it's never nearly as frequent and not nearly as widespread. Chelsea got a bit of it at their peak but not City levels of it(everyone on the enemies of football hyperbole train). Yes, Newcastles spending has been reigned-in with the regulations but it still feels like they are getting off very light, with the state owned aspect. It seems quite a lot in the MSM don't feel the need to mention it. With City, it seems like they all push the same narratives, they sustain the stories longer and they rehash/repeat the same things more, to make sure they have the public repeating what they want them to repeat. The lack of balance just isn't comparable, from what I remember.
I still don't see any club ever getting to the same level because it's not really repeatable. Because of City's relationship with United and what happened to them during City's rise. There's only Everton I can think of, where that's even possible, to be fair. However, as much as I'd love City to be able to take credit, City aren't the reason United are in the state they are in. So, if that is the reason for the widespread biased coverage starting in the early 2010s, it just shows you how silly football can get. United are in fact lucky, that they had credit in the bank. Luckier still, that the rigged PL format and media backing, protected them and kept them relevant and so on(because they've been awful and have been ran terribly). United being relatively fine, in spite of all the things that have gone wrong, shows how rigged football is, post PL launch.