I'm not sure its entirely fair to say that's their plan has only begun, as SteamOS first released over 5 years ago in 2013. As best I can tell, it was originally a strategic hedge against Microsoft locking down Windows in some way that prioritized the Windows Store for game distribution. That never really took off for Microsoft, and Valve didn't do a ton of work try to try to market SteamOS.
Though certainly they've been doing a lot of work behind the scenes with Proton now. I'm not sure where Proton leads quite yet other than making their existing Linux user base very happy. It's certainly increased the stickiness for me.