"Transitions", as in, an independent little section or fill that bridges the gap between 2 distinct sections is honestly more of a thing in rock and electronic music.
This is something that was always a big topic around here back when I joined, but I actually think a lot of music is made worse by having these little 1 bar phrases and such between two different sections because it creates an odd (or even, depending on song) # of bars in a phrase and feels like it "resets" the tune to my ears rather than creates a flow into the next section.
Like listen to these examples of orchestral or cinematic tunes:
None of these pieces have anything I would specifically call a "transition". It just goes one section into another. They do however pay attention to two things:
Anacrusis, and voice leading.
An anacrusis is a few notes before the first measure of a phrase that "lead-in" to it. A very common variant is that, in a minor key, you might have played the 5th and the minor 7th before playing the root on the downbeat of the first measure of the phrase.
Voice-leading refers to how the voices (instruments) or lines move to another pitch. You want to avoid creating too many "leaps", that is: movement larger than a major third. You want stepwise motion as much as possible.
So let's say that: Sections A and B are both 8 measures long. The melody note in the last bar of section A ends on the root, an octave below where you started.
This means that section B should ideally start in the new, lower octave rather than having the melody jump all the way back up. If I do go back up into that higher register for the beginning of section B, than I would create an anacrusis leading into that pitch, with a different instrument(s) above the previous melody in the last bar of section A. Also, if you come back to the tonic chord in the last bar before a new phrase, have a quick chord change on the last beat or couple of beats in the last bar so that it will smoothly lead back to the tonic, or whatever chord begins the new phrase.
You can use percussion like timpani and cymbals rolls to accent this or ramp the tempo a bit, but basically: There is nothing terribly special you should have to do to make two sections, even very different ones, flow into each other well if your voice-leading is strong.