I see two options. The first is to have your tile person straighten out the edge of the tile. Fabricate a reducer that's 1/4" thick i.e. the difference between your wood and tile), finish to match the floor and cut it to length. Undercut the door stops to the height of the tile so the reducer will slide under. Fill the gap between the wood and tile with something that's the thickness of the wood. Apply a little construction adhesive to the bottom of the reducer and install it, weighting it down until the adhesive dries. This can be done by closing the door and sliding wedges under it. The second option would be to use a matching baby threshold that would lip over the tile and hide the uneven edge. Fit it, fill the void, undercut stops and secure with adhesive. Trim the door bottom if needed. The bottom of the baby threshold might have to be shaved off so it sits level. If it's made for a 1/2" floor and your difference is only 1/4" you'd have to shave off 1/4". The first solution yields the lowest stepover height but is more work. The second is easy but has a bigger hump at the doorway.

the ideal way would have been to left a gap at the wood and then fill with a caulk. that way it wont impede the wood from expanding. Now ive seen lots of floors that didnt do this and they do fine for many years without issue. I think you will be ok, but it is fixable if it ever does become an issue.

THis is just a summer cottage, no insulation, heat, etc. it was built by a farmer for my parents 50 + years ago. The pine floors aren’t even tongue & groove, just very irregular boards, and I have no interest whatsoever in the time or expense of refinishing them. The vinyl plank is purchased; my only question is about the type of thrasition to orde.

Shim up the nosing to the tile height. Add a scotia to cover the gap on the underside. The tile installer could have taken care of it for you.