Just install this relay and parallel the coil with the generator input.
https://smile.amazon.com/gp/product/B07FCJFGL9/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
Hook the power center to the operating points, the shore cord to the normally closed and the generator input to the normally open.
Switches both the hot and neutral. Wire the grounds all together.
Easy and passive so you cannot forget.
Housted
2019 Forrest River Forrester 3051S 2014 Honda CRV toad.
1000 W Solar, converted to 50 amp
400 Amps of LiFePO4,3000 Watt Inverter, Refer converted with JC refrigeration unit, Sofa replaced with 2 swivel chairs, over cab bed converted to TV mount and storage