A comprehensive list of the Bohemian Rhapsody references in Wanderer’s character:
His previous name, Scaramouche, is mentioned twice in one lyric of the song.
His statement of, “I wish I'd never been born at all.” from the 3.3 quest trailer, his More About (Wanderer): IV voice line, and in-game interlude quest correlates to a well-known line from the song: “I sometimes wish I’d never been born at all.”
The Raiden Shogun’s name is Beelzebul, referencing the lyric: “Beelzebub has a devil put aside for me.” with the devil referencing the Wanderer.
His character demo video, found here, is titled “Wanderer: Any Way the Wind Blows.” This phrase is the ending lyric from Bohemian Rhapsody.
Similarly, in his voice line Feelings About Ascension: Building up, he says, “The wind is blowing this way,” referencing the same line as before.
The lyrics “So you think you can love me and leave me to die” and the repeated mention of a “mama,” whom the song is being addressed to might refer to both the Wanderer’s experience of being abandoned by the Shogun as well as the perceived betrayals that came after.
In his Least Favorite Foods voice line, he states, “I'm no fan of Dango.” This alludes to the ever-quoted lyric in relation to his character: “Scaramouch, Scaramouch, will you do the Fandango!”
His knowledge on the real nature of the stars and sky that he gained from the Unreconciled Stars event can be summarized with: “Is this the real life? / Is this just fantasy?” along with various other lyrics from the song.
His Fallen voice line: “Everything... was futile...” might be referencing the reoccurring line, “Nothing really matters.” This line may also be relevant to his knowledge of the sky.
The trailer for the Unreconciled Stars event, his character drip announcement, and his first appearance all occur on the anniversary of the song’s release. (Sourced from an Anon)
The domain that he was abandoned in after his creation is called Caught in a Landslide, which is another lyric in Bohemian Rhapsody. (Sourced from @kindleln in the replies)
In the 3.3 interlude Archon quest, Nahida near-quotes the lyric “Is this just fantasy?” by saying “This is just a fantasy.” She says this in a conversation with the Wanderer. (Sourced from @hemlockalope in the replies)
Scaramouce’s boss battle theme from before when he became the Wanderer is titled “Let’s Do The Fandango!” As stated before, this references a fairly iconic line from the song, especially as this occurs while he is still identifiable under the name Scaramouche. Similarly, another theme called “Ominous Fandango” is played during the Unreconciled Stars event, in which he was first introduced. It is worth mentioning that the Fandango is a sort of dance, which can apply to the mentions of a dance he performed when he lived with the sword smiths of the Raiden Gokoden. It is also an insult meaning fool, which makes sense when compared to how he speaks to others. (Partially sourced from @changing-shades in the replies)
Please let me know if I missed anything! I will add it to the post as I compile more information.