Leave the 3-way switch alone!
Colors don't mean half as much as you'd like. Actually, they are there to distinguish wires in cable. Only ground has a reserved "color", though if present, neutral must be on white.
The red wire is nothing but a pigtail, it could be purple for all it matters. People tend to make pigtails with any old bit of scrap they have lying around.
Actually on this switch, both the screw and the backstab are in use, which is sloppy but it means the black backstabbed wire and the red pigtail are connected. So all of these are connected together:
- the black wire going to the backstab on that plain switch
- the red pigtail going from that wire nut to the plain switch
- the black wire going from that wire nut to the wall
- the black wire going from that wire nut to the smart switch.
I would rend the wire out of that backstab and put it under the wire nut, as this will make the wiring easier to understand. And also because the backstab and screw method is bad, and also because backstabs are lousy in the first place.
So now, the clump of blacks (and red pigtail) are almost certainly the supply hot coming into this box.
Now it becomes clear: the solitary black wire on the switch is the switched-hot wire going to the receptacle.
You can take it from here, I trust.