They make a single transfer switch for $100 that will work for the furnace. Or some furnaces have a plug into a dedicated outlet so you just plug it directly into the generator. Here is the transfer switch I have: Reliance Controls TF151W Easy/Tran Transfer Switch for Generators, Small, Gray https://smile.amazon.com/dp/B000HRWG8U/ref=cm_sw_r_cp_api_glt_fabc_CGW1AGM88AQN8S90FVRF
I think what you are looking for is a generator transfer switch. You (or I recommend an electrician) would wire this up next to the RV circuit breaker and select the circuits you want to be able to toggle between grid power (when connected via the outdoor outlet), or your EcoFlow (when off grid) which plugs into the transfer switch.
Single Circuit:
https://www.amazon.com/Reliance-Controls-TF151W-Transfer-Generators/dp/B000HRWG8U/ref=pd\_lpo\_2?pd\_rd\_i=B000HRWG8U&psc=1
4 Circuit:
https://www.homedepot.com/p/NATURE-S-GENERATOR-15-Amp-120V-4-Circuit-Indoor-Non-Automatic-Power-Transfer-Switch-Kit-HKNGPTK/307780505?g\_store=&source=shoppingads&locale=en-US&&mtc=SHOPPING-BF-CDP-GGL-D28I-028\_037\_OUTDR\_PW\_ACC-...
Do you mean something like this transfer switch ?