This does not mean that there will be no government shutdown or prolonged CR this time around. Congress can only do so much. There's another branch of government whose headquarter is at the other end of Pennsylvania Avenue. Some experts think there will be a government shutdown, mostly over the President's insistence on tens of billions of dollars in funding for a border wall. Even most Republicans aren't eager for that wall, much less a government shutdown over it, but the President believes it vitally important. He may even think it's just what he needs to get Republican voters out to the polls in November. I'd call that nuts but I'm not a Republican voter.
Whenever an appropriation bill gets passed, it's almost certain to be bad news for Social Security. Both the House and Senate passed appropriations bills give the Social Security Administration $11 billion in operating funds, which is what the President requested, but which is $400 million below the appropriation for the current fiscal year. The cut is even worse than it sounds, however. You have to consider inflation which is about 2.9%. Social Security needed an increase of about $330 million just to stay even. The agency will effectually receive a 6.4% cut in its operating budget. That's going to hurt.
If you want the best case scenario, it would be that despite the appropriations progress already made, we'll still end up with a CR and that the CR will extend past the start of the new Congress next January and that Democrats will control one or both Houses of Congress which will allow them to make demands with a higher appropriation for Social Security being one of their demands. I don't think that's going to happen. If nothing else, Democrats winning one or both Houses of Congress would concentrate the attention of Republicans who would rush to enact appropriations bills before their power diminishes.