I would never even attempt to unwrap this kind of polycount. You also don't need this level of detail to get a smooth surface. I would recommend you remodel this with a much lower polycount.
Once this model has lower polycount, it will be much easier to unwrap. You can use Seams or automatic unwrap. You use Seams by selecting edges, go to edge menu and ...
When the object has no UV map (see in the Object Data Properties) then there are no UVs to sync.
To get a UV map, hit U to unwrap the object or at least the Plus-button next to the UV slots to add one.
Just apply location and scale of the armature with Ctrl+A, Location and Ctrl+A, Scale - or just use 1x All Transformations which applies also the Rotation.
Location should be (0, 0, 0) and Scale should be (1.0, 1.0, 1.0) in the N-panel's Item tab. The same data can be found in Object Properties > Transformations.
Do the same for the Scale of the mouth ...
Select the Image Texture node with the bake image in both the 2 materials like you've done. Note that if your material is 100% metallic it won't be able to bake any diffuse, just black color, this is what's happening.
This starts off by taking a slightly different approach than Đặng Hải Phụng and make the coordinate space of your plane stretch over -1 to 1. By default this will just tile the UV.
Then we use a Vector Math -> Absolute node so that negative numbers are treated as positive. This gives us a mirror effect on each axis.
To find the offending UV section, go to the UV Editing tab, and in the top left of the screen, enable UV Sync Selection (the button with the two arrows). In the viewport on the right, enter edit mode, and select the face(s) that need re-sizing/re-orienting. Note this only works properly in face select mode. With the Sync enabled, your selected face will be ...
You have select sync turned on.
Nothing is wrong here. The mesh components are touching in 3D, and since that option is on, blender shows the whole UV map. Any pseudo-duplicate vertices that are on the border of two patches and thus part of both get selected as one.
Turn off select sync to avoid undesired effects from this.
Note: Sorry I didn't read your questions carefully. You already worked out this solution, but I'll leave it here for others to have a look.
here's another approach:
First start with what the texture space should look like? With the understanding that Blender maps the texture (0-1) onto the texture coordinates (0-1), and the texture coordinates being 0-2 due ...
Because blender allows colors and Vectors to be interchangeable in some cases (Both are Vec3 Containers), you should be able to get away with mixing your vectors using MixRGB Nodes blocked off with masks (exemplified in my image by the Separate XYZ and Greater Than Math nodes on the X and Y axis). Using a combination of mapping nodes to orient the initial ...
just like Caroline, I'd recommend that you retopologize the model, it's really not that hard, but if you still wish to work with this model, I'd suggest you manually unwrap it.
What I'd suggest that you do, is click on one edge, hold Ctrl, click on another edge, what this does is, it selects the shortest path between them, then you could mark it as a seam