The only game I can think of to do this as a part of the main story very well, rather than as an optional “Score relationship points to earn this person as a meaningless prize” is in Trails in the Sky 1+2. Old game by now, but it really stuck with me.
The challenge is to involve character relationships in the story itself, in ways you don’t expect; have that person who fell in love with the main character lie to protect them from a murder charge, and then be arrested for treason; have a villain that takes one love interest hostage, only to realize someone else cared even more about them and is far more dangerous, etc.
I'm not sure you'd call it a slow burn but I really enjoyed how the relationship developed in Prince of Persia: Sand of Time. Pity we never got a proper sequel.
Xenogears is my favorite romance story in gaming. Amazing depth to it.
I also liked the Bastila romance plot in Knights of the Old Republic. Some neat Force shenanigans going on there. Tali is my favorite self-insert Bioware romance, though.