I honestly don't think Sony cares. GT isn't going anywhere and Forza winning awards doesn't really impact their bottom line. The series did for them what it needed to, and with a new, proper, release (GT7/8/whatever), they will probably get things back on track. It is a massive brand and they need to abandon much of what went wrong with Sport.
With their new push on 1st Party content, I wouldn't even eliminate the possibility of a new racing property altogether, but considering they just took home the biggest GOTY award around, again, I don't think they're losing sleep over Forza winning best racing game in a year where they didn't even release one.
It all depends how you look at the awards. In terms of popularity or sales or quality everyone is going to have there own opinions. There are also many GOTY awards that get given out at different outlets. Weather you take The Game Awards, Gamespots, IGNs or the 200 others seriously.
The point here is that Forza has been left unchallenged through-out this entire generation and even when it had competition it basically didn't matter because it over came the challenges and basically took the racing genre on themselves. If you are a racing fan than this will peak there interests more than the other awards. Different taste for different people I suppose. I am a huge Blizzard fan yet I didn't care about OverWatch winning GOTY because OverWatch just isn't for me, instead I found other games that year I loved more.
You are probably right, maybe Sony don't care as much as they use to in the racing genre, probably the same way they don't care about the FPS genre either as GG moved away from Killzone. I feel Sony has found there strength in the 3rd person action games. Its something they do really well in, much like how Xbox do really well in the FPS and Racing market and Nintendo in the Platforming market etc. Each company has there strengths which is good for the industry.