Is there a Cliff Notes version of how to get the 2022 Nautilus Panel to siphon/allow water to work in the faucets with an air lock condition?

This is assuming that you are trying to get water flowing inside the coach when you have the levers set in the “Dry Camping” positions and water doesn’t flow when you open a faucet or flush the toilet. Yes, there is – authored by William Byerly Holt:
To Fix Nautilus Panel pump air lock.
1- Set panel for Winterize syphon;
2- hook up hose to city water supply, fill the hose with water, then connect to the water panel;
3- open a faucet;
4- turn on the hose and pump until water flows smoothly at faucet; you should hear a change in the pump sound once it is pumping water.
5- Turn off faucet and pump, then hose;
6- reset panel as needed;
7- Disconnect hose.
8- Tightly seal the hose connection with the provided cap.
Never set the White lever horizontal unless you are going to run the pump with a hose connected, making sure you have liquid in the hose at all times. Always fill a syphon hose before turning on the pump. Do not let the syphon hose go dry while the pump is running.
Make sure hose connection is TIGHT at panel.
Always put the cap on the panels hose input when not in use. Make sure it is tightly seated.
Make sure all levers are fully switched to their positions so they will not cross leak.
For a new system, or anytime the water tank goes completely empty, you should purge any air from the system. First, Power Fill the tank. Then switch the panel to Dry Camping and open each water tap individually for both Hot and Cold water, [faucets, toilet, inside/outside showers], until you get a good flow.

Where can I find information about the Nautilus Water Panel installed in 2022 or newer Travatos?

Right here, in this document prepared by Shaun Simpkins.

2022 Travato Water System notes and diagrams – V1 Shaun Simpkins