Walls – Is this a load-bearing wall between the house’s entrance and dining room

The only thing bearing on that wall are shampoo bottles. Knock away. The wall is empty. Note that the end of the porcelain tub is open, so something will have to go back to cover it up. When it's open you can inspect under the tub for horrors.

But you'll also want to remove the wall sheathing all around that tub, and read up about flashing and backer board.

Determining if this segment is load bearing should be evident to a competent contractor. There are a few things to look for. You have to look above and below the wall in question. In the floor or attic above, you have to determine if there is structure bearing down directly or via headers to this wall segment. Next, you need to look below in the basement level to see if a beam, post or other structure is directly below the wall segment carrying the load to the foundation. While not always true, this wall segment may be load bearing if it is parallel to the longest dimension of the house, usually perpendicular to a gable end and located half way between the two longest exterior walls. There are a few methods of framing that could make this a load bearing wall, even if you have full trusses for roof support, ie; ceiling joists that rest on a center beam directly over the wall in question. As I said, most competent carpenters could look at this and determine it's load bearing status. Obviously, a set of plans would be helpful as well. Even if it is load bearing, a good carpenter will be able to design a header to span the new opening, support the load and allow you to remove the section of wall you want gone.