There's a few things we can try before the amputation.
Firstly, I'd clear your network cache (in your options in GTS). Then I'd try a full power cycle on everything from PS4 to router and anything in-between - not just turn off and on again, but turn off, unplug and leave it for a few minutes before plugging it all back in and rebooting.
It's also worth checking your internet connection - although online play doesn't appear to be an issue, it's not something to totally rule out at this point. Check the connection settings, make sure you haven't migrated to NAT1 of NAT3. If you're not wired in, wire it in. If you're not on a static IP for the console, fix it to a static IP - and put that IP into your router's DMZ.
Has anything changed since the last time you got a DW car? New ISP for example?