I'm trying to figure out how ... crazy I can get with the formatting of my campaign page. Things I personally would like to see is a multipage format for campaigns personally, but for the time being I was curious what language it uses to format things in, and how robust is it to handle things like html or markup or the like.

to my knowledge, the text boxes on the campaign page do not support html or markup.  I think you are limited to the editing tools provided, which are essentially the same as those here in the forums.  So you can formate text (bold, underline, etc), change text alignment and color, bullet points, etc.    

For extensive notes, the notes section is pretty unwieldy, but it can be helped by judicious use of spoiler blocks.  I finally shifted to using a Dropbox Paper document for my notes, though.

Quote from ArwensDaughter >>

to my knowledge, the text boxes on the campaign page do not support html or markup.  I think you are limited to the editing tools provided, which are essentially the same as those here in the forums.  So you can formate text (bold, underline, etc), change text alignment and color, bullet points, etc.    

For extensive notes, the notes section is pretty unwieldy, but it can be helped by judicious use of spoiler blocks.  I finally shifted to using a Dropbox Paper document for my notes, though.

 This was informative thanks. I was hoping for at least the ability to break out columns or something, but c'est la vie. The campaign page has a lot of potential but it definitely needs more functionality or customization .

Without a comment/topic function, do people just play by post in the forums?

Yep, there's a dedicated subforum for play by post; https://www.dndbeyond.com/forums/d-d-beyond-general/play-by-post

As a correction to what has been posted above, yes you can use HTML in the campaign notes boxes and in forum posts, and homebrew description boxes.

To access HTML click the </> icon and you will see your comment HTML. Here you can use basic HTML to format and change the post. Click the </> icon again to exit "HTML mode" and see the changes in effect. This can be great for using spacing and formatting not easily accessible with the WYSIWYG editor, great for copy-and-pasting stuff without the forum's auto-formatting making it wonky and for making tables.

Quote from Cyb3rM1nd >>

As a correction to what has been posted above, yes you can use HTML in the campaign notes boxes and in forum posts, and homebrew description boxes.

To access HTML click the </> icon and you will see your comment HTML. Here you can use basic HTML to format and change the post. Click the </> icon again to exit "HTML mode" and see the changes in effect. This can be great for using spacing and formatting not easily accessible with the WYSIWYG editor, great for copy-and-pasting stuff without the forum's auto-formatting making it wonky and for making tables.

 Thank you for the correction!!