The punctuation surrounding quotes, including direct speech, tends to be a compromise. For instance, a comma is used where a full stop might reasonably be expected:
"I need the car today," said Jill.
Here is the 'rule' for the situation with OP's first version (I think it makes sense):
When you plop a speaker tag right in the middle of someone’s
conversation, make sure that you don’t create a run-on sentence:
Wrong: “When you move a piano, you must be careful,” squeaked Al, “I
could have been killed.”
Right: “When you move a piano, you must be
careful,” squeaked Al. “I could have been killed.”
So two sentences (the second not needing another speaker tag) rather than a semicolon or comma. The perhaps reasonable-looking use of the semicolon is non-standard.