In the Infinity Saga, the music of the MCU was sometimes somewhat lackluster. There are movies that serve as exception though. Captain America The Winter Soldier, Guardians of the Galaxy and Black Panther being among them. They have recognizable music, and show that music -both as themes and pop songs- can be used to set a certain atmosphere for scenes or even a whole movie.
In general, the MCU has little continuity in character themes. Like with Iron Man or Thor, who get new themes every movie they appear in. A simple explanation could be the continuous reinventions the characters go through and that the new music can be seen as a reflection of these reinventions. Some themes are reused in places. Black Panther's theme can be heard in Avengers Infinity War, and Captain America's theme can briefly be heard in Avengers Endgame.
Marvel Musical Universe
In Black Panther, themes use sounds that are reflective of the characters' backgrounds and arcs. Black Panther's theme is very recognizable, using drums to reflect T'Challa's kingship and African heritage. It's used many times in Black Panther, and makes it return in Avengers Infinity War as well when entering Wakanda. Another recognizable Black Panther theme is that of Killmonger. His theme is more technological and hip-hop focused to reflect his background of growing up in the United States (1).
Another character that has a recognizable theme is the Winter Soldier. It's theme is even more technological than Kilmonger's. It also reuses sounds. Bucky's scream when falling from the train in The First Avenger was taken and the sound was mechanized, which also reflects the now-mechanized Bucky himself. Moreover, this theme is not only used to accompany the character, but also to signify what is about to happen: it's time for Captain America to run. Because when it's a fight with Bucky, it's not a fight to win, but a fight to survive.
Songs can be used to set a mood as well. In Guardians of the Galaxy and it's sequel, music is woven into the narrative. Vol. 1 uses 'O-o-h Child' as part of Peter Quill's identity, and Vol. 2 uses 'The Chain' even as part of the whole team's identity (2). Using songs with narrative weight, unlike what Suicide Squad did, songs can be used as an extention of the story that can result in especially strong musical moments, which can also be seen in other Marvel movies like Into the Spider-Verse (3).
More musical moods
Original songs can be used as well to propel the story and give identity to the characters, as shown by musicals like Tangled. Shrek does something similar, but uses pop songs instead (4). Critical Role has both in Vox Machina and it's adaptation. Albeit the latter's original songs are to prevent copyright issues. The score alone however sells the setting, whether that is medieval in Tangled, fantastical in Shrek, a life of piracy in Assassin's Creed IV, or a whole array of musical settings like the animated Avatar shows.
Connecting themes to places and objects is also done in Lord of the Rings and The Hobbit. Although it no stranger to original songs either. In many different places the very distinguishable themes associated with The Shire and The One Ring can be heard. And not just when those things aren't on-screen, but instead are looming in the background. As such, many of the individual themes can be heard in the main theme, as it's all part of the overall story, even when they aren't directly present.
Lastly, themes can also be connected to ideas. In Star Wars, The Binary Sunset has become the theme for the force entire. The sequel trilogy especially relies heavily on reusing themes and reframing in this way (5). While on the other hand, the original trilogy tends to replace an old theme with a new theme. New ideas can also arise from old ideas, giving room to new themes. Avatar uses music to vaguely connect to familiar concepts as well. It manages to sound tribal and alien, even if it isn't (6).