Both are short length dramas with a real world FL entering a fictional historical world and unexpectedly falling in love with the emperor ML who is the main character in the world. Both MLs have invulnerability of a sort (plot armor as the main character vs. an immortal body) that leaves toward the end as the FL messes with the plot. Both dramas have a guide who gives tasks to the FL and only she is aware of/can see.
Both have a real world FL entering a historical setting game world and falling in love with the emperor ML who is a fictional character in that world. Both FLs complete the game and return to the real world, but out of love for the ML they choose to return to the game and spend their lives with him.