After the release of Half-Life 2 episode 2,( with the cliffhanger that I have too much of a heart to spoil), fans were begging for half-Life 2 episode 3, and so was Valve. In fact, they were already making it. But, just at the beginning of development Valve did something they do a lot nowadays - they got bored. Valve’s development team can only go so far before they get bored, and Portal and Half-Life had been their only projects for well over ten years.
They started working on other things: new engines, new consoles, VR, and updates to previous games. Until early 2020 Half-Life 3 had become more of a meme because people genuinely thought it wouldn’t happen. But then they announced that they were going to make a prequel: Half-Life: Alyx. Since then people have been satisfied, especially because Valve supposedly has another Half-Life game in the works. Half-Life: Alyx retconned the first cliffhanger and replaced it with another one. But now the idea of Half-Life 3 is less of a myth and more of a fact.
Half-Life 3 may never happen, but as long as Valve keeps up these projects we still have hope. In the meantime, however, the Steam Deck, Valves’ very own handheld gaming console (like the Nintendo switch) is going to release, or depending on when this article is live, has already been released.