This is not law. I think it's unlikely to become law anytime soon. This bill passed the PA Senate but would need to pass in the House as well and have the governor sign it into law. I think it's unlikely to pass in the House and, if it does, I think Tom Wolf is likely to veto it.
I know Philly and the state have a disagreement about whether open carry is legal in there without a permit as it is in the rest of the state. Concealed carry has always required a permit. In 1989 PA became a "shall-issue" state. That is the discretionary judgement of bureaucrats and other officials were removed from the process. You either had objective background issues like criminal convictions, active indictments, involuntary commitments or protection orders as concrete reasons not to be issued a permit or you got one if you applied. Shall-issue is the format I personally prefer. Right now 21 states are shall-issue and 21 others are unrestricted which is the measure that the PA Senate passed.
Historically Vermont is the only state to have always (for 200+ years) been unrestricted. Essentially this means that carrying concealed without a permit is not a crime.
In the unrestricted states a background check is still required to buy a gun at a gun store. A few states also have laws on the books requiring folks that buy from private sellers to pass background checks.
To answer the question, "Can anyone carry?" that's a yes. In unrestricted states it is still a crime to be in possession if you are a prohibited person. Here's a link to the list of who would be a prohibited person: https://www.atf.gov/firearms/identify-prohibited-persons
So yes anyone can carry openly or concealed but for some folks to do so in some places is illegal. The folks who usually do those sorts of things generally don't really care about it being illegal.
There are good and bad things to say on both sides of the "unrestricted carry" issue. I personally don't like it. I am convinced that I will never have the time or money to be informed, practiced and skilled enough to consider carrying at all except for maybe in some extreme wilderness setting.