You are correct.
Article III, Section 3 of The United States Constitution states, “He shall from time to time give to Congress Information of the State of the Union, and recommend such Measures as he sall judge necessary and expedieny; he may, on extrodinary Occasions, convene both houses, or either of them, ...”
Don’t believe that SotU is an extrodinary occasion although Harry would more than welcome Zero to the Senate.
And, just because he can convene both houses, doesn’t mean he gets to speak to them assembled.
Giving the president such a huge bully stage is pure drama.