Just to clarify, there are no dedicated servers operated by anyone. All games on console are strictly person to person: you hosting a friend on your game or them hosting you on their game. Sony maintains the network code which allows Playstations to communicate with each other and THAT is what it sounds like is down right now and not working for some games. Most likely they updated some things and now they will be slowly but surely bringing compatibility for the games on their network that didn't like the change. This happens all the time with graphics card drivers on the PC. Sometimes a new driver gets released and a game you have doesn't like it. It isn't on the developers of that game to get their game compatible with the new driver, it is up to Nvidia to bugfix whatever edgecases excluded those particular games. Users will often have to revert to an older driver while they wait for the fix.
Unfortunately, in your case, you just have to wait until Sony finishes fixing all their edgecases. I'm sure there is probably a way to report problems to Sony so that they know that they need to test 7 Days to Die on their network. They still sell 7 Days to Die on their store so they are obligated to still support it on their network. (Unless they print a disclaimer that MP is no longer supported and the title is a SP title only)
Finally, there will no longer be any more updates to the current console version of 7 Days to Die. It is now like hundreds of other PS4 games that are "as is" and not perpetually being updated. Even if 7 Days to Die sells another 30 million copies, not a single dime of that will be used to update the current version. It will ALL be pumped into the PC game, the next PC game, and the next PC game, and--- MAYBE a new version of 7 Days to Die for PS5 (but no guarantees of that.)