I'll just trust you on the first part. I know Stalin got complaints (which also indicated that the scale was pretty big) and didn't act on them, and that's why I said he was negligent. If I remember right, Yezhov was honey-potted by a foreign power* and it used that to blackmail him (though of course sodomy was on the list of charges), but he absolutely was convicted on the basis of being a wrecker and trying to damage the SU by killing many people to destabilize it. Whether it is true that he was a wrecker or he was actually just a fall guy for a reckless operation, I don't know. He definitely did also at one point admit to what he was ultimately convicted of, though he later claimed that he only did so under torture and was in fact innocent of most of those charges.

Per NATOpedia:

In his confession, Yezhov admitted to the standard litany of state crimes necessary to mark him as an "enemy of the people" prior to execution, including "wrecking", official incompetence, theft of government funds, and treasonous collaboration with German spies and saboteurs. Apart from these political crimes, he was also accused of and confessed to a humiliating history of sexual promiscuity, including homosexuality, rumors that were later deemed true by some post-Soviet examinations of the case.

On 2 February 1940, Yezhov was tried behind closed doors by the Military Collegium, chaired by Soviet judge Vasiliy Ulrikh. Yezhov, like his predecessor Yagoda, maintained to the end his love for Stalin. Yezhov denied being a spy, a terrorist, or a conspirator, stating that he preferred "death to telling lies". He maintained that his previous confession had been obtained under torture, admitted that he had purged 14,000 of his fellow Chekists, but said that he was surrounded by "enemies of the people".

Again, I think the truth of the matter is unclear due to the relevant archival evidence not being open, but this is what the story is.

*I thought that was him but I'm having trouble finding it. I don't think it was Yagoda, even though he too seemed to be what we would call bi, but it definitely happened to someone . . .