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I don't recall anyone saying there were more votes than registered voters in an entire state. So then they give as their example some statewide numbers. The AP is lying.

Actually, this was said. A claim of more votes than registered voters in an entire state was made and widely circulated on social media, and thus found its way into print. For example, a pro-Trump columnist on an Israeli website wrote:

"Later in the day, both Wisconsin and Michigan flipped to Vice President Joe Biden. I was informed at noon that Wisconsin reported a 101% voter turnout (3,129,000 registered voters with 3,170,206 counted). That suggests that the same voter voted more than once. In 2016 Wisconsin also had voter irregularities and Donald Trump was awarded close to another 1000 votes that had either not been counted or were blocked in some way.

"In Michigan 105% of registered voters voted (5,453,000 registered voters, 5,736,581 actually voted)."

Link: https://www.israelnationalnews.com/News/News.aspx/290646

A UK source reported that Donald Trump Jr. also picked up the charge about Wisconsin: https://news.sky.com/story/us-election-2020-donald-trumps-voter-fraud-claims-debunked-12132000

The AP story in the OP did address the actual charge made in Pennsylvania, namely that the official tally of votes added up to more than the number of voters. The story then went on to refer to "similar claims" based on the number of registered voters (as opposed to the number of people who showed up to vote). The story did not impute those "similar claims" to the recent Pennsylvania report, but gave the data on registered voters just in case anyone made the claim about Pennsylvania, given that it had been made about Wisconsin and Michigan.

Incidentally, the claim about Wisconsin arose because someone carelessly used the figure for registered voters as of the 2018 midterms. If you aren't meticulous about all the details, you can end up creating a false charge that discredits the whole enterprise.

The big flaw in the AP story is the omission that others have noted. If the state's response is that the compilation of the data hasn't yet been completed, a reporter should ask the obvious follow-up question: Why not?