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Depends on what the poster is. If it's still mostly text content, just arranged in a certain way, then by all means you can. For example:

https://typst.app/universe/package/poster-syndrome

And here's one for foldable cards:

https://typst.app/universe/package/keepsake

(Not endorsing those specific packages, they're just the first ones I managed to find)

For more free-form layouts, I just use Inkscape. It has built-in PDF export which works great. I assume other similar tools like Figma or Illustrator would also work well.

Probably not. As you point out, it's a typesetting tool like LaTeX, not a page layout tool.

You could probably write a template that does the right thing, but that's true of LaTeX as well.

I do use them to make flyers and other PDF content.

You can see an example on my LinkedIn account I posted last week when travelling (it's in French). https://www.linkedin.com/feed/update/urn:li:activity:7472526...