Except, why are the dems going harder if this is showing he has more support?
Two reasons I can think of, that seem most probable. Might be a combination of both.
1) They genuinely think that he can't win. They want him to be the candidate, because they are betting it'll be a repeat of the midterms, rather than a repeat of 2016. The assumption is that moderates just hate Trump too much, and that even if the lawsuits create sympathy, enough people will be repelled by the notion of a "Criminal-in-Chief", so that they'll vote Democrat.
2) They genuinely are suffienciently out of touch that they believe that the lawsuits are making most people dislike Trump, and that this is a good way to smear him further. They kept doing this with the impeachments and the collusion hoax, so it fits their earlier pattern of operation. Also, note that Hillary figured that calling working Americans "a basket of deplorables" was a good move, demonstrating that, yes, the Democrats really
are out of touch.
As things currently look, their positions are misguided, and their efforts are actually helping along Trump's campaign. They turned him from "reasonably disgraced in the eyes of many" to "an obvious victim of persecution". Public sympathy tending towards the underdog, they could have rendered him no greater service.
There appears to be a dawning awareness of it, too, but they're committed now. If they drop the persecution, he can claim that as proof that they had nothing substantial, which
also improves his electability. So it seems that they final strategy is going to be an attempt to use various convictions to block him from running. Specifically, they want to convict him of "engaging in insurrection or rebellion" (Jan 6th), and then use section 3 of the 14th amendment to disqualify him from holding office.