There was even a minor character in My Little Pony with a "mane bun", first introduced in June of 2016, so pretty much exactly ten years ago. Zephyr Breeze, Fluttershy's younger brother, based on the younger brother of writer Michael Vogel.

Zephyr Breeze's whole shtick was that he was a slacker/freeloader who gives up on everything he tries, is broadly useless and annoying and causes problems for others, has an overinflated ego, and makes uncomfortable romantic passes at Rainbow Dash when it's clear that she does not care for him in the slightest. At the same time, he was training to become a mane therapist/stylist, and his voice and mannerisms were sort of flamboyant or gay-coded, so there was definitely a Gender element to it. Hate for man buns definitely has a lot of overlap with anti-"metrosexual" or anti-"hipster" type "imagine cleaning your ass" sentiments.

The end of the first episode Zephyr Breeze appears in has him get over his crippling fear of failure, and he becomes independent and finishes his education and all. The only other episode Zephyr Breeze prominently appears in was in 2019, where he's become a member of the royal guard, but still makes uncomfortable passes at Rainbow Dash.

So yeah, there were definitely stereotypes around "man buns", if they even showed up in kids' cartoons.