I'm sure there must be another phrase but I just can't seem to find it. I'm not looking for a word to replace "unsung", I prefer a completely new phrase/idiom that expresses the same meaning. Thank you.
Although it's not gender neutral (that might not matter), there is backroom boy.
From The Phrase Finder:
What's the meaning of the phrase 'Backroom boy'?
One who works in anonymity in an organization while others take on more public roles.
What's the origin of the phrase 'Backroom boy'?
First used to describe the anonymous technicians and scientists who worked behind the scenes in the UK during World War Two. Lord Beaverbrook coined it in a speech in March 1941:
"Now who is responsible for this work of development on which so much depends? To whom must the praise be given? To the boys in the back rooms. They do not sit in the limelight. But they are the men who do all the work. Many of them are Civil Servants."
It's also still in use relatively recently.
From the 2018 article "A week the Ontario PCs will live to regret" by Richard Forbes (emphasis mine):
… Certainly, there’s a market out there for the angry populism that Ford will sell to Ontarians. Like a bull in a china shop, he stands to do a lot of damage within his own party, attacking the legitimacy of Vic Fedeli and Caroline Mulroney (a popular contender) as a ‘backroom boy’ and a ‘centrist plutocrat,’ respectively.
From the 2019 article "'Not the usual way?' On the involvement of an East German couple with the planning of the Ethiopian capital" by Monika Motylińska e Phuong Phan (emphasis mine):
The Baumbachs were more in line with the gendered stereotype, with Peter being the one in the spotlight. Ute’s role was similar to that of Edwin Maxwell Fry, who has been described by Iain Jackson and Jessica Holland as the “backroom-boy.”
Depending on context, if you use the phrase, you might want to put it in quotation marks to highlight its informal use.