I assume Parappa and other characters from pure musical games are out of this specific conversation.
I won’t post it in too much detail since it’s a memorable moment one can experience in a relatively recent game but that moment in Elden Ring (typically near the Weeping Peninsula) when you hear somebody singing for the first time, and try to find where the singing comes from, comes to mind. Pretty clever use of a diegetic song inside a video game.
Another iconic “diegetic singing” moment from this generation: Mayor Pauline singing during the New Donk City festival in Super Mario Odyssey. I have questions regarding the proper use of taxpayer money for re-election campaign purposes in New Donk City.
A character in Disaster Report 3 sings at least twice in the game. On mobile I can't copy link at the correct time so scrub on over to 1 hour 20 to enjoy.
I can think of a few games where characters have sung a song in the game‘s lore, like how Julia is the singer of “Eyes on Me” in FFVIII’s world or how Red sang “The Spine” in Transistor. There's also non-lexical vocable performances like this one
Also sorry it's only fair to include the superior Polish version of “Wilcza Zamieć” (whose literal translation “Wolf Blizzard” is so much funnier than the official localized title lol) as well: