I would select both, press Ctrl J to join, press Ctrl A and choose All Transforms, and add a remesh modifier. You’ll need to turn the voxel size down to maintain your structure.
Actually what I would personally do is retopologize your structure by hand, that’s going to take a lot longer if you’re not practiced, so that’s a last case option here
You don’t need to remesh, but if you want your shape to be “attached” to the model, you do. It really depends on what you’re going for. You could always try scaling down the screw threads so it looks like they’re part of the underlying geometry
I would personally start with the spout, and create that out of a BOLT from the included extra objects…(you have to activate it ) …delete the head and bottom faces the extrude the inner ring down through the screw portion…then model out the lower bottle shape…and make sure that the bottle is Manifold ( would hold water and not leak) you can activate the 3d print tools ( included ) to check your mesh…