Newbie: wiring a light switch
I do not see a ground wire although that is possible, a ground is normally a bare copper in residential wiring and it would be attached to a green screw that is normally part of the metal mounting yoke.
I believe I see a black with some white paint crossing from one switch to the other this should be a hot.
Since you have a red wire I would follow that back to the cable it enters the box in if there is a black wire in that cable it probably also goes to the fan I regularly wire rooms like that so a fan light combo can have 2 switches letting us know more about the wiring will provide better answers.
Ground to 2 switches totally normal green or bare copper is normal.
A white coming to the switch that has power all the time this is called a switch leg the white is getting the power from the ceiling fixture and it is hot.
If you have a white hot all the time then the red and black should go back to the same fixture and they control the light or fan.
White is normally neutral but in a switch leg it is always hot required by code.