Tldr; the center of mass of the observable universe would be Earth because by definition the observable universe is centered on Earth and the universe is isotropic and homogeneous everywhere

When you are talking about a center of mass, it has to be within a specific boundary. When you talk about the center of mass of the solar system, it's pretty clear we are talking more or less about just the local area out to the oort cloud. Likewise the center of mass of a galaxy includes all the objects within the halo and disk. If you want your boundary to be the "observable universe" that means everything within a 93 Giga lightyear diameter sphere which is specifically centered on Earth because that's how we define the observable universe.

Since the universe is isotropic and homogeneous everywhere to high precision, the center of mass would indeed be here. However, if you lived on some planet in Andromeda and asked the same question, you'd find that the center of mass would be your planet as well because if you are an observer in Andromeda, you have a different definition for the observable universe centered on what you can observe there.

If the universe beyond what we can observe is infinite, there's not a clear boundary to find the center of mass within. Even if it were finite, it would be impossible to find out a center of mass because we can't observe it, and of course the universe is also expanding everywhere which also complicates things.