Electrical – How to install vanity light – wall box has 2 white, 2 red, 2 black, 2 ground wires

Sounds like you have one black hot wire coming into the box (probably that bottom one), which passed through a hot over to your bedroom switch.

So my guess would be that you should have two of the blacks wirenutted together -- that would be the hot wire coming in to the box, and the passthrough to the bedroom light. Also in that bundle should be two pigtailed wires that go to one pole of your 2 switches.

Then the other pole of the switches would be connected to the remaining black wires. The white neutrals should remain bundled together as they are.

It looks like the ground wires also have loops in them for connecting to screw terminals, you should make sure that all of the ground wires in the box are connected together with a wire nut so you have an uninterrupted ground even if there are no switches connected, then pigtail off of that bundle to connect to the ground screw on your new switches.

Here's a diagram showing my guess at how the hots should be connected:

Though this is only a guess -- an easy way to identify which one is the hot wire would be to tape or wirenut the exposed ends of the wire and leave them hanging out of the box, turn on the breaker, then use your non-contact voltage sensor to see which one is hot.

There's no easy way other than trial-and-error to identify which ones go to each bathroom light and which one goes over to the bedroom.

Oh, and do remember to connect the ground to the new switches since you have a plastic box (even if the previous switches were not grounded) - I think it's required by code now, but even if not, it's a good idea - especially in a bathroom where wet hands will be touching the light switch.

This is a bit more annoying than it looks (spoiler: the obvious way to wire it may not pass muster with all inspectors)

The power feed to this all comes in at box 1 (vanity light) and feeds the /2 switch loop to box 3 as well as the /2 feed to box 2. Box 2 and Box 3 are connected by a /3 cable, apparently intended to be a switch loop.

With all this, you'd think you'd be able to:

1. Turn the power off, of course
2. Connect the white wire from the /2 in box 2 to the white wires from the light and fan there.
3. Connect all grounds together in box 2 and to a box ground pigtail (if it's a metal box)
4. Connect the black wire from the /2 cable in box 2 to the white wire in the /3 cable and mark that white wire as a hot (permanent marker as you have done should be fine -- it just needs to be a permanent/indelible marking, visible from all angles).
5. Connect the red wire from the /3 cable in box 2 to the blue wire from the overhead light.
6. Connect the black wire from the /3 cable in box 2 to the black wire from the bath fan.
7. Connect all the grounds in box 3 together.
8. Connect the white wire from the /3 cable in box 3 to the HOT terminal on the fan controller after marking it as a hot.
9. Connect the black wire from the /3 cable in box 3 to the 1-POLE terminal on the fan controller.
10. Connect the white wire from the /2 cable in box 3 to the switch HOT terminal, again after marking it hot.
11. Connect the black wire from the /2 cable in box 3 to the switch 1-POLE terminal.
12. Connect the red wire from the /3 cable in box 3 to the other switch 1-pole terminal -- the Adorne parts can terminate two wires on each terminal.
13. Button everything back up and turn the power on.

and have it work. In fact, it will work if you do this; however, there's a catch! This arrangement takes one switch loop feed (from the vanity light) and returns it back down two different cables (to the vanity light and to the overhead light), which can be seen as a Code violation (of the 300.3(B)/310.10(H)/300.20 complex) as it creates a large loop area that puts out stray magnetic fields in your bathroom (good for ruining the picture on that old TV you have mounted in the wall in there ;).

A more conservative approach would be to utilize a dual pole switch to break the two hot feeds simultaneously while sending the return paths back the way they came, as follows:

7. Connect all the grounds in box 3 together, and to grounding (green/bare) pigtails to any switches that need them.
8. Connect the white wire from the /3 cable in box 3 to two (preferably black) pigtails after marking it as a hot. One pigtail goes to the HOT terminal on the fan controller and the other goes to one side of the dual pole switch.
9. Connect the black wire from the /3 cable in box 3 to the 1-POLE terminal on the fan controller.
10. Connect the red wire from the /3 cable in box 3 to the other terminal on the same side of the dual pole switch as the pigtail.
11. Connect the black wire from the /2 cable in box 3 to the other side of the dual pole switch.
12. Connect the white wire from the /2 cable in box 3 to the other terminal on the other side of the dual pole switch.
13. Button everything back up and turn the power on.

This arrangement also works, and keeps the two light switch loops neatly separated. However, Legrand does not make a two pole Adorne switch, and I do not believe there are faceplates available for the combination of an Adorne device side by side with a standard switch in a two gang box. You'd have to get a standard-form-factor (i.e. not Adorne) fan controller to do this.