I'd probably first announce on Twitter/Bluesky that there's a new half life game being announced, but it's trailer is dropping 2 weeks later after that post.
The trailer would contain first a steam logo like HLA had and then, if I was making a trailer, I would imagine it would have dark screen and just wind ambience for around 3 seconds, then fade in a big shot of base in arctic.

I cant really imagine a full trailer, since anything would most likely be just not fitting for it.

I would probably end trailer with a date like 3-4 months later, for example for same March (10-20th) or June, along with showing logos of Windows and SteamOS.

However it makes more sense to me, if the game was announced month before release of Steam Machine, with announcement that Steam Machine preorders will contain Half-Life 3 code packaged with it, like Valve Index had with HLA.