Combine tiled and untiled parts in material (texture)

You need to set the lod to 0 and choose to merge materials (not on by default)

Single mesh with multiple mats:

Left mesh after merging materials:

Unreal generates an atlas like this for the merged variant:

It’s not perfect as it physically repeats the texture inside of the atlas, but to get the atlas you want you probably need c++ at that point.

Edit:
Have a look at this thread regarding tile-able atlases

Using this type of tile-able atlas along with vertex colors to define the material lerp you can get this

This gives

vertex color for mesh

1 texture only for the mesh

The x and y of the vector next to the texture coordinates dictates the amount of repeats in X and Y of the tileable texture.

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