There is nothing actually syntactically wrong with using a semicolon in a conjunction like that, but it's nonstandard, and it looks a little strange.
Typically, it's just commas that would be used. Semicolons are used in the specific case where one or more list items are already punctuated with a comma—making it confusing if commas are also being used to separate those individual items.
From The Chicago Manual of Style (17th ed.), 6.60:
When items in a series themselves contain internal punctuation, separating the items with semicolons can aid clarity. If ambiguity seems unlikely, commas may be used instead.
The membership of the international commission was as follows: France, 4; Germany, 5; Great Britain, 1; Italy, 3; United States, 7.
The defendant, in an attempt to mitigate his sentence, pleaded that he had recently, on doctor’s orders, gone off his medications; that his car—which, incidentally, he had won in the late 1970s on Let’s Make a Deal—had spontaneously caught fire; and that he had not eaten for several days.
Marilynn, Sunita, and Jared, research assistants; Carlos, programming consultant; and Carol, audiovisual editor, provided support and prepared these materials for publication.
Notice how in all of those examples, there are individual list items that are punctuated with commas. Those commas do not denote the end of one list item and the start of another.
As Chicago says, a semicolon is recommended in this kind of situation.
But when there isn't any chance of confusion, commas are the more common device used to separate list items.
A good reason to not use semicolons when commas on their own do not present ambiguity is that most people associate semicolons with the division of independent clauses. If I'm reading the sentence in the question, I don't see any any commas being used, so I assume that what the semicolons are separating are not list items but independent clauses. However, by the time I get to the second semicolon, I realize that's not the case. I have to back up and read the sentence a second time—this time parsing it not as two independent clauses, but as a single clause with three list items. This makes the reading experience awkward. Had commas been used, I wouldn't have had that problem.