By people whose full-time job is tracking his lies, you mean journalists? This is a story from the guardian and was presumably written by journalists. Not sure what you mean by sources outside the fediverse. I feel like I'm missing a thread in this conversation.
Second thing: It is a bribe by US federal laws, which usually cover the promise of an exchange as well as the actual exchange, c.f. 18 U.S. Code § 210 - Offer to procure appointive public office:
Whoever pays or offers or promises any money or thing of value, to any person, firm, or corporation in consideration of the use or promise to use any influence to procure any appointive office or place under the United States for any person, shall be fined under this title or imprisoned not more than one year, or both.
"Bribery" is also commonly understood to start at the offer, not at the consummation of the deal, at least in my experience. I don't know how common that is in different US states, or if it's that way outside the US.
Beside that, impeachable offenses don't have to be crimes defined by US law, whether a given offense is impeachable is solely in the hands of congress. I actually think this is a good thing to try an impeachment over, it's a blatant offer of a quid pro quo and Trump is getting so unpopular that Republicans might be willing to finally ditch him and pretend they never knew the guy. Who knows though, I've been half-expecting the Republican party to drop Trump and get a new standard bearer for six years now, and they keep not doing it, so clearly I don't have an accurate read of the situation.