The two-part epoxy that someone mentioned is made by the 3M company. You purchase an applicator and then the D-100 cartridges and mixing nozzles for it. Any good hardwood floor materials dealer should have it all in stock. The cartidges are not cheap...about $10 each. The applicator was about $20 when I bought mine. I don't know what they cost today. You could also use Timbermate floor filler in white oak color. However, I would recommend testing to see how the color out of the box will stain with your chosen stain. Timbermate also is something you get at a flooring materials dealer.

Ahhhhh...now we get where the tacky boards are coming from. I'm going to bet the 20 planks are gathered in a select area. And I would bet my left kidney that area, downstairs, corresponds to a higher humidity. Before they come back and attempt another fix, I HIGHLY RECOMMEND you bring in another dehumidifier (you may need more than 2 to keep the basement in the 45% range) and get it running in the CORRESPONDING area of the basement. In other words, drop that baby directly below the tacky spot in the floor. Run it for SEVERAL DAYS before asking the guys to come back in. Let us know how it goes.

"Tom Silva replies: You can do it either way. My painting contractor, Jim Clark, wants to be last so doesn't have to repaint baseboards that have been splotched with stain or ployurethane, or nicked by a sander. Besides, even the most careful flooring contractors inevitably leave a film of dust everywhere, he says. My flooring contractor, Pat Hunt, sees things a little differently. He prefers to be last because floor finishes take a while to fully cure, so he doesn't want anyone walking on them even when they're covered with protective tarps. He also says it's pretty common for other contractors to damage or spill stuff on a finished floor. The way he figures it, it's much easier to touch up paint than a floor finish. As the general contractor, I sometimes have the flooring finisher go first, and sometimes I let him go last. It all depends on what's best for the project schedule. I have that kind of flexibility because I know Clark and Hunt will put a lot of effort into protecting the other guy's work." https://www.thisoldhouse.com/ask-toh/what-comes-first-wall-painting-or-floor-refinishing

I don't know about other contractors but every refinishing proposal I send out states "does not include any touchup painting or a complete dust cleanup. The edge sander has to be used right up to the perimeter trim so it's difficult to do a nice job without making some marks. If we're staining, the base can be masked, but the stain can get drawn up between the trim and tape, then harden. If paint adhesion is questionable, masking can end up pulling off large areas of paint. This is especially true if latex has been applied over oil without the necessary preparation. If I'm challenged on this practice I specify that I haven't added a penny to the price to do touchup painting and that they should be prepared to repaint the perimeter trim and door surrounds. OTOH, if someone has finished cabinet toekicks or bases, fancy faux finished base, marble base etc., we will mask it off and work around it by hand. We charge extra to do so, with the reasoning that it's cheaper than refinishing or replacing something that gets stained. For regular painted trim I feel it's cheaper to repaint than it is to mask and do extra work, plus assume the extra risks dealing with questionable paint. Your picture indicates that you probably need shoemold to cover the gaps under your baseboard. If it was mine I'd sand the base really well, test the adhesion of the existing paint (since the chips shown in the picture look questionable), and paint the whole thing.