It looks like a drain line out next to the condensate drain line in. I have seen these drain up through the roof next to the flue, a plumbing vent or a roof vent (among other places). There is a device or option which will turn the furnace off if the tank does not empty. I sometimes recommend they have one of those.
The plastic tygon hose is the discharge from the pump which is float activated and will discharge to god knows where I would have followed the hose to see where it went. Not an uncommon install at all if no drain opening are available
BTW did that foam strip at the top of the return air box completely seal the return air off from the burner area of the furnace. That kind of a return usually get my attention as it is a poor set up that kind of foam usually does not last long and creates problems
That’s a relatively common installation in homes that were not originally built with A/C (cooling) systems. I often see these tapped into a plumbing vent or routed to laundry sinks and stand pipes.
You should recommend periodic monitoring to ensure the pump remains operational, and that there are no leaks in the discharge system.
Ditto Jeff.
Very common in finished basements when the plumbing drains are not close to the units. They usually are pumped outside or to another fixture drain. Not worthe the cost of plumbing a seperate drain line to the units for the amount of condensate.