Chosen Solution

After hooking up a new utility sink to existing roughed-in plumbing, the bowl of the toilet nearby will not hold water level. (The toilet in the other bathroom is fine.) I suspect the new additional drain is the issue but do not understand why or what to do to remedy it. The bowl fills but does not swirl and swirl normallly, and the water level starts to recede immediately, emptying to a minimal level in about 10 seconds.

The drain pipe needs to be able to vent air via something like this. Otherwise the toilet will not function properly.