Master override light switch complicates smart light switch installation?

I moved into a home built in 1975 last week and there is a most interesting switch behind the door in the master bedroom. It appears to override the light switches in the entry way, upstairs landing, living room, laundry room, and kitchen (three switches in the kitchen, including one that controls the hardwired dishwasher). Several of those lights are actually 3-way switches as well. When the master switch is off, all other light switches function as expected. If I turn on the master switch, it overrides all the other light switch settings and they all turn on. When I turn the master switch off, they return to their prior settings (if a light was on before turning on the master switch, it stays on; if it was off, it stays off).

This isn’t a feature I would want or use, but I could just ignore the switch. However, I want to install smart switches in almost every location that is currently controlled by the master switch, and since I don’t understand how they are currently wired to do this, I’m wondering if that complicates anything.

One other minor annoyance is that I use the master switch, all the lights flicker and it appears to also cause a brief loss of power to the dishwasher. I think it causes the dishwasher to lose its cycle. Not a huge issue if I don’t use it, but annoying.

So my questions are:

1. Can I remove this feature completely, possibly by simply removing
   the switch from the master bedroom and capping off some wires or by disconnecting certain wires from the individual switches?
2. If it can’t be removed, is there any harm from ignoring the master switch (pretty easy to do) and installing smart switches in the locations I want them?

To answer questions asked by P2000: Yes, you are correct. When switched on, the master switch turns on all lights I mentioned no matter how their switches are positioned. When I turn the master switch back off, they return to their prior state no matter what that was. No basement here but there is a box in the garage between the main panel and the house. I’ve attached a picture below.

Adding photos as requested:

This first photo is the master or override switch located in my bedroom. Looks pretty normal to me. Just the line/load connected, no traveler or anything else. Neutral and ground in box but not connected to switch.

The next three photos are different angles of the switch for the entry. This is a 3-way switch. There are a total of four wires connected: a red, a white, and two blacks. The red "hops" over to the other switch in the box that is for the porch light just outside (this is the only switch for the porch light so isn’t a 3-way switch). Neutrals appear to be bundled in the box as well as a ground but again are not connected to the switches.

This photo is of the other end of the 3-way switch for the entry light. It has three wires connected: a white, a red and a black. No neutral or ground in this box.

This is a picture of the box in the garage. Haven’t opened it up; it’s up high. Maybe there are some sort of relays in it?