be satiated, eat one's full
饜 centers on reaching the limit of eating: being fully satiated or having eaten one's fill.
饜 combines 厭 (to be satisfied, to tire of) with 食 (food/eat), reinforcing the idea of eating until satisfied or full.
Inside the enclosure 厭 (which suggests satisfaction or weariness), there is 食 (food). Picture eating so much food that you become completely satiated and cannot eat another bite.
For エン, imagine an endless banquet where you eat until you are full: endless -> エン, and the food 食 inside 厭 keeps coming until you are satiated.