Thermostat Wires not in App

Photos show my wiring. Y/O wire not in App or videos. I have the C Wire adapter connected, but I also have a small transformer under my power switch that is connected.

When I flip the switch my fan comes on and the Wyze keeps clicking, nothing is displayed.

This is weird. The green wire at the thermostat is attached to G, but at the furnace,green is attached to Y. And the Y wire at the thermostat is blue. Is there a splice somewhere in the wire where these colors get switched? Please show how you have wired the C adapter.
The old thermostat has terminals that can be used for multiple functions, depending on what system they are attached to. In your case, the wires are as follows, from left to right:
Green : G
Red : Rc
Blue : Y
White : W

At the furnace panel, the red wire on Y and the white wire on C should stay where they are, and assuming the green/blue wires get swapped somewhere in your wire run, the terminal strip on the C adapter should have the red wire from R on the R terminal, the green wire from Y on the Y terminal, the blue wire from G on the G terminal, and the white wire from W on the W terminal The C adapter’s ribbon cable should be connected to the furnace’s control board, so there should be 1 wire on W, R, and G, and 2 wires on Y and C.

No splice that I’m aware of but we only moved into this house one week ago.

The red wire from the transformer was connected to the far left the white wire from the transformer was connected to the far right.

I tried it with a transformer connected and with the transformer disconnected.

Thankfully the thermostat and the furnace are about 6 ft apart. I can run a new wire if necessary and for testing purposes I could just run it straight across the hallway from the furnace to the thermostat I just need to know what colors need to connect to what. Once it tests out and is working I can drag the wire up the wall through the ceiling and then down to the thermostat.

Your outdoor A/C unit is probably spliced into your blue/green thermostat wire somewhere. You will need to give it it’s own wire run back to the furnace board, or run a C wire directly from the furnace to the thermostat and not use the C adapter.

What do I do with the wires from the Transformer attached to the power switch? White was connected to C on the furnace board. Red was connected to Y on the furnace board.

I’m yet about clear as mud now on which wires connect to what terminals at either end of the cable. And you are saying I do NOT need the C wire adapter?

Is there some connection back to the outdoor A/C unit I need to make somewhere?

The transformer attached to Y and C is essentially the “Rc” transformer. This is a very odd way to wire a system. If I were you, I’d run new thermostat wire from the furnace to the thermostat.

Here’s essentially how your old thermostat was hooked up:

Here’s how you want the wyze to be hooked up:

What am I missing, I don’t know what those other terminals connect to (see annotations).

The item with Y and C terminals is your outdoor A/C compressor and condenser.