Is it academically dishonest to submit the same project to two different classes in the same semester?

Whether it is or not, the professors in the courses will have the last say. If either of them considers it dishonest or otherwise improper, for any reason, you will wind up in a bad place.

But there is an easy way out. Just ask both of them for permission to do this. They might say yes, or no, but then you have a clear answer. They might also give permission provided that you go a bit beyond the bare essentials to demonstrate sufficient work (and seriousness) to cover both.

But doing it without notice or permission seems dangerous, no matter the ethics.

And, you can even come off looking good on this if you actually make an offer to do more than the minimum and submit the result to both. It might mean a bit less work for you overall, and might also teach you some things you wouldn't otherwise have learned. Even for a previously submitted project, offering to extend the old work can be a plus.

FWIW, I would probably be inclined to permit it, with the proviso of some added requirements.

And, I actually did this in secondary school because I changed schools. I asked an instructor at the new place if I could submit a report that I'd previously worked on, but wasn't actually graded for (since I left). I was given permission and it saved me a bit of work.

This was actually encouraged in the university I attended. The lecturers were of the opinion that the goal is to learn, not to make projects. If one project can teach you the skills required for two courses, why do two projects?

An example of a project I used for multiple courses was a bit of software I developed as a volunteer activity. I used this for the course in which we had to learn to gather requirements, in the course in which we learned how to develop complex software and in the course that worked on the soft skill of communicating with a client.

I don't think it's dishonest in and of itself, but it is not okay if there are rules against it, obviously.

Yes [if without explicit permission], and it is against many (most?) Student Conduct Guidelines

For example, at Montana State University, this is covered under "Multiple Submission" under Policies and Procedures (under Academic Honesty):

F. Multiple submission - submitting the same paper or oral report for credit in two University courses without the instructor's permission; making minor revisions in a paper or report for which credit has already been received and submitting it again as a new piece of work.

Every University I've worked at has had similar policy wording, and I can't think of any others where I've reviewed related sections of their policies where similar wording wasn't present, but I certainly haven't done an exhaustive search on this specifically.

The key provision here, of course, is "without the instructor's permission". If it has been discussed and approved, it is likely fine at most institutions (check the specific policies and procedures for your University or College, do not assume on this). It becomes academic dishonesty when it is not approved.

Work that is submitted for a course is expected to have been done for that course, not simply the student taking other work previously (or even concurrently) done and submitting it, even if they were in fact the one who did the work. Failing to discuss submitting the same work to multiple courses is an act of academic dishonesty, in the ethical sense at the least, as the student is not meeting the expectations of their actions in regards to the coursework for each individual course.