The best way to wrap a video around a 3D text cylinder

You can't wrap any texture around a 3D Text cylinder. I'll try to explain. [This is one of my most major requests concerning 3D Text — the ability to specify how to apply textures to a surface ***without*** changing the way things are already set up. As a kind of added on feature. It's one of the very few things that would have been needed in order to avoid adding USDZ 3D Objects ... ]

This is what happens when you wrap a texture on a 3D cylinder:

This is the original texture (16:9 1920x1080):

What happens is there is that the texture is blended by "quarter" — 2 forward and 2 in reverse. You can see that the pattern is also offset somewhat. To make it even worse, the quarters aren't even lengths - 2 are longer and 2 are shorter.

How to get around it (no pun intended):

You need an adequate rectangle character like this one:

▐ (unicode 2590). Make a string: ▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐▐ (enough to span the width and closely fill the "aspect" needed.

Wrap the text on a circle path. You need to rotate the characters 90º on the X-axis from the Font Format inspector (not Properties > Transforms!) Adjust Tracking if necessary so all the parts touch. Rotate the text Group -90º to show the front. You can use Path Shape > Radius to make sure the texture lines up where the edges come together in the wrap.

This is an example of the same "texture" wrapped:

You can see that the pattern is wrapped (more) correctly.

This looks a little chunky but it can be mitigated a little bit by "lighting" and view angles. Otherwise, use narrower characters. You can use as many characters as you like and the more you use the smoother it will look.

I have assumed you know how to apply images (/video) to 3D surfaces in 3D Text... about the Placement > Scale parameter and all that. Fitting the video/image/texture across the "string" of characters will be accomplished via Placement (including offsets). [This stuff pretty much works differently with every different character, so there's no set of straightforward instructions.]

I'm sure I've left out some stuff. 3D Text has so much depth, so explore. I recommend setting the Depth of the 3d characters to 0 and the Edges to Square. If you're really good at seeing the arch, then you can use Round for the Front Edge Size. Keep the Depth shallow and expand the Width to help make the outer circumference more round.

HTH