I think a lot of the special sauce with the Half Life games is their "Show don't tell" approach to game design.
You load up the game, watch an intro (for games after HL1) and boom you're in the game. Nothing is going to appear on your screen beyond your HUD except for one time tips when acquiring a new weapon and chapter titles when progressing to a new level. Everything happens in real time and everything always happens from the POV of the player. There are no cut scenes, there are no cinematic transitions, and the player's POV is never intercut with cameras/external perspectives.
It makes the games feel grounded and more cinematic, IMO. Its a game design language that really puts the onus on the player to witness the story and game for themselves. When I play a Half-Life or Portal game, I feel like I'm discovering the story as I play, while other games often feel like I'm being presented or shown a story as I play. The execution is more nuanced than that, but the game's simplicity makes it difficult to focus on anything other than the story and world within the game.
When you look at the stories of each Half-Life game, each game tends to follow the same structure with the same kind of plot points. But for me, it never feels repetitive because the experience of witnessing the story is different for each game. Of course Half-Life isn't the only game that does this and this of course isn't the only reason why Half-Life has been enshrined as one of the GOATs.
The underlying content of the game, its aesthetic, the textures and models, sound design and score, voice acting, ect. all are great in Half-Life, but I wouldn't say that Half-Life is the best at any of these things. I also wouldn't say the game's narrative is the best of the best either. Despite this it remains my all time favorite game franchise, possibly/probably because I grew up with it but also because the game does a fantastic job of using that underlying content to give little clues. Everything feels like it has a purpose, whether it is apparent in the moment or not.
But I am just a storyteller that happens to be a barely competent programmer with absolutely no experience in game development, so all of this is just my opinion based on my own experience!