What do you do if you have developments on your paper during the long peer review process?

Wait until the first revision to introduce this changes and let the editor know that you did not exclusively modify your original manuscript based on the reviewers comments?

Yes, that's the most common thing to do.

Of course, if the paper is rejected, then you can incorporate the changes before submitting somewhere else.

If the new developments are dramatic, then you may instead decide to leave the original paper alone, and write a separate paper with the new work.

This depends a lot on the scale of your proposed changes. If they are huge, you might have a new paper to follow on the first. If they are really small, as you suggest, you could just save them for a revision, supposing that the paper will be "accepted with revisions".

The intermediate case is a bit harder. If the changes alter the thrust of the paper or a major conclusion, you need to inform the editor. In the long run that will save time, in most cases.

But yes, you can and should point out things in the revision that weren't in the original to make the second round of review either go faster or be avoided.