All sounds like misinformed bullshit, to be honest. I can see Valve prototyping game systems integrated into a first person shooter, much like the rumours of Half-Life going open world, to disrupt the existing formula. But outright reimagining the entire franchise, and a mainline entry at that, as an RTS or advanced adventure game sounds pretty ludicrous.
Even if there's an essence of truth to these claims, I'd interpret this more there being prototypes of noted that existed within the Half-Life universe; a Half-Life RTS, a Half-Life adventure game, etc. There's likely a hundred oddball prototypes of varying genres across their existing franchises given that's how Valve's development pipeline operates. None of them gained traction, thus none saw fruition, but all kinda exist in a void of Half-Life technical stuff.
I'm sticking with my existing assumptions; due to excessive crunch and franchise burnout a majority of developers working on Half-Life needed to take a break and work on other projects. Momentum never returned as the production costs for a traditional Half-Life game in the modern market ballooned, internal expectations/desire to see the third major entry do something original never caught traction via prototypes, much of the team was lead off/convince to work on other more profitable projects, and the production culture at Valve shifted to titles that favour a more open communal approach hence the focus on multiplayer.
Half-Life is dead and will never return.