Why didn't Valve ever talk about Half-Life 3? Simple: A new Half-Life game hasn't been in development for quite some time.
Half-Life: Alyx marks Valve's return to proper games development, and more importantly, a return to the series altogether. But why did it take so long? Why didn't we ever hear about any other Half-Life projects? According to Valve's recent Reddit AmA, these projects simply didn't exist until now. Half-Life was pretty much in stasis for the longest time as Valve focused on its VR hardware endeavors and managing the billion-dollar Steam storefront.
"We didn't talk about Half-Life for a long time because we weren't actively working on a Half-Life game. Once Half-Life: Alyx became a reality internally, it was already clear to us that this was something we wanted to involve the community in. We're going to be doing more of this in the next few weeks as we prepare to launch it," the devs said in the AmA.
Conversely, the same is true for Left 4 Dead. Despite tons of rumors and datamined info, Valve didn't talk about Left 4 Dead for so long because they haven't worked on the IP for years now. Valve recently confirmed Left 4 Dead 3 isn't in active development.
Half-Life: Alyx is just the beginning for the new Half-Life resurgence. Valve plans to make more games in the landmark sci-fi FPS series, and will use the VR-exclusive as a bridging point/testing grounds to flex its new world-building prowess, iterate on its Source 2 engine, and generally collect feedback.
In short, Half-Life: Alyx is just a waystation on the road to Half-Life 3.
Half-Life: Alyx releases in March 2020 and is a VR-exclusive game. It's compatible with all Steam VR headsets including Oculus, HTC, Windows Mixed Reality, and Index-branded HMDs.