Is the floor there on a slab or crawlspace/basement?

@Kendrah Yes, I think you are correct about the type of pipe. Thanks for the quick response!

@sktn77a This is the lower half of a split level, so I believe there would be concrete below the flooring here. Not positive though..

Well, if it's on a slab, you'll need to jackhammer a trough to the sump for the condensate drain under the floor before you lay the new flooring.

You need a little inexpensive sump pump that will pump the condensation water up and through the wall to the sink drain pipe of the half bath.

The pipe in question is condensate drain that can inexpensivly be ran overhead simply by installing a pump which is common in situations like this. As for concealing ductwork and other pipes, dropped ceilings and/or fur-down chase are solutions.

Before redirecting the condensate into another drain, I'd want to know if the furnace is a high-efficiency, condensing-type furnace. If so, it may be necessary to keep the condensate drain segregated from the home's DWV system or to install a neutralizer to address the acidity of the condensate--particularly if the home has a septic system.

It looks like a condensing vent rather than B-vent (because they went wild on wrapping the foil insulation on it). Looks like they wrapped the lineset and probably the cat too.

As said, you can get a condensate pump. Determine if you can poke through an exterior wall right there instead of going to the Laundry floor drain. Also make sure you have clearance/access around the furnace.