Hmm.. I tried a test where I moved all Regions to the right by 4 bars and then dragged the Markers to match and it worked fine. I was also able to do it in one step: I created 4-bar Cycle at the beginning of the song and used the Tracks (Arrange) pane Edit menu command Cut/Insert Time > Insert Silence at Locators, which moved all the Regions and the Markers to the right by 4 bars.
I tried the same thing with Arrangement Markers -- the same things also worked, though with a caveat or two. Using the Cut/Insert Time command worked fine, but dragging the Arrangement Markers by hand to match the position of already-moved Regions was more of a pain in the ass -- Logic wouldn't let me drag the Arrangement Markers all at once (though it went through the motions); instead I had to move the start and end point of each marker one-by-one (back-to-front).
However, after I added Arrangement Markers to the Project, the regular Markers also refused to let me drag them, and odd things started to happen (Cycle ranges changed on their own, Logic counted bars incorrectly and located to the wrong bar..!?!) Btw, I'm in LP 10.5.1 on Mojave -- maybe there are some bugs in Arrangement Markers in that version..? I don't really use markers in general, but I'll be staying away from them (especially Arrangement Markers) for sure now..