In the UV editor, click the Synch icon after you select the face. It’s the 2 arrows pointing different directions. Then do the mirror. In newer versions of blender(I believe 4.3 or newer) instead of of having to turn off synch there is a shared location drop down to the right of the 4 selection mode icons. You can click it and change it from shared to disabled. This will allow you to flip the selected face or faces and not affect the vertices of the connected faces.
