The short answer is that it doesn't. The closest form of romance available to players in Genshin Impact is the hangout quests introduced after the 1.4 update.
Despite presenting extensive stories set in the mythical region of Teyvat, Genshin Impact does not have a romantic angle. There are certain voice lines in the hangout events that can be categorized as flirting. Apart from that, there have been no aspects of in-game characters being portrayed in romantic scenarios.
Although introducing the new housing system with the 1.5 update has caused various speculations regarding the introduction of romantic aspects in the game, miHoYo has provided no information regarding the possibility.
This could also mean that the developers are solely focused on improving the stories portrayed in Genshin Impact. Here's everything to know about the possibility of romantic scenarios being introduced in Genshin Impact.
Possibility of romantic scenarios in Genshin Impact
Despite featuring certain scenarios in the hangout quests with a date-like vibe, Genshin Impact does not present any direct options for romantic scenarios in the game.
Since miHoYo is based in China, where LGBTQ+ visibility in pop culture is scant and controversial, it seems obvious that the developers wouldn't want to draw regulatory attention.
Having said that, the possibility of a dating simulation mini-game or other romantic scenarios in Genshin Impact is extremely bleak. However, considering the uncountable requests for romantic scenarios in Genshin Impact, the developers could develop a method that wouldn't resonate with everyone.
Nevertheless, players will have to make do with the "feel good" vibe available in a few possible outcomes via hangout quests until that happens. With that in mind, Genshin Impact has a lot to offer through Teyvat's stories.
With extensive stories and quests to complete, there is a lot that the game has to offer for players. Genshin Impact was never meant to be a dating simulator or a romantic experience anyway.