Switch – dimmer light switch with secondary constant 120V output

Many dimmers have an adjustment for the minimum level. You don't mention what type of dimmer you have but you can consult the instructions on how to adjust this. As @dslake mentions in his answer, adjustments might be via a knob or screw, but if it's digital, it could also be a button sequence.

Needing to perform this is more common with electronic dimmer switches since they need to work for many different types of bulbs (incandescent, CFL, LED).

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.