Part of the mesh is not moving along with the rig in pose mode even though its one mesh

Question

the whole character is one mesh, not parented to each other, just straight up joined together. when I rigged it, I assumed the shoulder armor with move with arm rig. I'm stuck now :'<

Here is the blend file if you guys want to check

Answer 1

A quick test of whether automatic weight painting worked is to select the character; enter weight paint mode; and enable the Zero weight All setting in viewport overlays:

In your case, this shows that the shoulder pad armor isn't painted in any Vertex group:

To fix this, you must apply weight painting to the shoulder pads to match the bones and they should follow. The left pad, for instance, should probably move when the left shoulder moves. The bone name for the left shoulder is DEF-shoulder.L so select the Vertex Group with the same name and edit it:

I suck at weight painting, so I'm going to cheat. Back in edit mode, I island select (shortcut L) the left shoulder pad while I still have DEF-shoulder.L selected. I then go to vertex groups and select assign. Back in weight paint mode the shoulder pad now looks like this, because a weight of 1 shows up as all red:

Now when I rotate the shoulder bone the pad rotates with it.

Do the same for the right pad and DEF-shoulder.R and both pads now work.

Of course, you may want to have multiple bones, especially the upper arms, influence the shoulder pad, so you'll probably want to weight paint it for multiple vertex groups.