Lying under oath was also what got Bill Clinton impeached, and that too is "just words".
That said, the claim that this unduly influenced the previous election is, IMO, probably incorrect: that Trump is a philanderer was known in 2016, and his conviction for these offences was known by the 2024 election, and yet he still won.
The way I heard it, the government used a specific language for "have sexual relations with" (hereinafter HSRW):
A HSRW B if the mouth, hands, or genitals of A touch the genitals of B.
Any hackernews regular would notice that HSRW is not associative - as in it is entirely possible for A HSRW B to be true, but B HSRW A to be false; in fact this was the case for if A's mouth touches B's genitals; A HSRW B but !(B HSRW A).
You can whine and plead and ask the question 4,000 times, but at the end of the day, if one don't understand logic, you might be a Republican Senator in the 1990's.
The trial court disagreed that these statements truthfully responded to the deposition, and fined him for his misleading answer.
For instance in Russia, their Supreme Court actually threw out the first conviction of Navalny on embezzlement charges. The local case itself was a shit show, but what else would you call a conviction in a case based largely on the words of a serial liar of undoubtedly near zero character, who also had a financial and vindictive motivation to lie? And I'm not talking about Navalny's case there, but imagine I was. Your opinion should not change if you're being logically consistent.
This is the reason that these trials sent Trump's popularity surging, and very possibly being the reason he won the popular vote. It seems that not only were they shit shows, but because they are seen as being motivated by the person being charged, rather than by the acts alleged.
FWIW, this does not mean he's innocent. It just means that if he wasn't who he is, none of these cases, all launched just in time to try to interfere with the election, would have happened.