Shadowdark was literally created for your situation, it is designed to be an OSR game with mechanics that will be familiar to 5e players.
As you said, it doesn't do anything completely new but it is one of the most elegant rpg systemsI've ever played. A wonderful balance of simplicity and richness.
If you're new to OSR styles of play my tip would be to embrace the fragility of life. Having character deaths be an expected part of the game can be quite jarring to players used to 5e. Consider running a "funnel" game where your players each have multiple "level 0" characters that go through a dungeon where most of them will die, and the survivors become your character pool. Its a way to get players to shift their mindset.
The Lair of the Lamb by the brilliant Arnold K is a great funnel dungeon: https://goblinpunch.blogspot.com/2020/04/lair-of-lamb-final.html
Feel free to ask any questions you might have.