I might share a slightly different way to go as I am sometimes disappointed in how much time I have to watch videos and then find out it was not actually correct on the fine points for my furnace as it was a different model.
Electronics and things like furnaces and thermostats change just as quick as cell phones and we do need to get the right info to pick up the right small points.
So I look at the item like the furnace or thermostat and search for brand and model info on that item .
Info from ten years ago is not likely to have good info on what is in your 2021 RV!
But a common item on many furnaces is the sail switch and it can be confusing.
Called a sail because it hangs down in the airflow that is used by the furnace to move combustion air for the flames in the vent and out the exhaust of the furnace.
You likely have two round holes on the outside wall near the furnace?
Cold air goes in one and comes out hot from the other! Inside the furnace there is a section where the fire is kept separate from the inside RV air which is drawn into the furnace, heated and comes back inside!
Like your home furnace, the fumes are not pushed into the house but go up and out the vent!
But there is a major difference in RV furnaces as a safety item.
In an RV, we don't open the gas valve and let the RV fill with propane if the furnace fails to light!
On RV furnaces the blower comes on before the gas flow starts. The sail switch "sail " hangs down into the combustion airflow and if that sail doesn't get enough air movement to make it close a microswitch, the gas valve doesn't open!
Normally the small Dometic types will try three times to get it right and if not, they go into lockout and shut down until the problem with the sail switch is cleared!
Not filling the RV with propane and then letting it light is a good thing! So the sail switch has to sail first!
Different brand but same idea!
But that doesn't seem to be the problem as you are not getting the right blower to come on when calling for heat. for some reason you are getting the air conditioner blower to come on first, so I suspect a thermostat or wiring problem!
Basic point is putting warm air down low as it will rise but cool air comes in up high and sinks!
Air should come in lower vents for a bit and THEN hear the fire light and begin to warm the air coming in!