They have been "working" on Half Life 3 for over a decade, with many promising leads found through datamining things left in other source games over that time. There is almost always absurd levels of speculation over the smallest crumbs of datamined material.

For example, there's been an unfinished NPC worked on for Episode 3 left in Half Life 2 that was first shown in a tech demo in 2006, literally prefixed with "Ep3_" in the code. It's been around for 18 years and the most that was used from it was graphics for the gels in Portal 2, vs all of the speculated things about it.

The recent documentary they released had what was effectively a post-mortem section where they talked about why Episode 3/Half Life 3 never came out.

I can see why you might think that their new controller and headset might be enough of a game changer that they feel like making 3 is worth it again, but the overall feeling I've gotten from them from following all of this closely since the pre-Orange Box days is that: 3 isn't happening due to the immense pressure and expectations that have built up over the many years people have been waiting. Maybe we get Alyx 2 or some other spin off, but the only thing they'd accomplish with 3 at this point is disappointing a wide variety of people with countless conflicting expectations.

At the very least you also have to contend with "Valve Time". What would take a normal studio a year takes them four due to their obsession with polishing everything. Team Fortress 2 started development in 1998 and didn't release for 9 years.

Don't get me wrong, I'm excited to see where they go next, and I hope this means more than a voice actor sending a fun new years message. But you need to understand that "definitive evidence" of 3 coming based off datamined material has been floating around for 15+ years now.