Purpose is key
I'll look at three purposes for this system, shifting along the spectrum of arcane/mundane. It also depends on how identifiable users are, and how easy editing is. How to access a server is also a question - do I just need a name, or must I have a piece of the server-crystal? The key feature of your wizards-only rule is that access has a very high bar to entry, but is cheap once you can do it at all.
5e wizards love their lore and spellbooks. Especially being able to get to new spells. This version of the magic-net operates at first like a library-index, with a brief (15w) summary of what is included in this index coming first and expanding into a list of topics and the proper keywords to request their subpage. A few hours of use can get you the full text of a spell to study. (This is the forerunner of the Wizard Mobile Library answer.)
Private servers will pop up to work on specific projects together before publishing (or without the Lords of Light snooping on your necromancy research). These will look more like an email server.
Field expeditions into dangerous places (i.e. adventuring) will use this to log what they can - and perhaps back up the field journal. These will look like ordered logs, unless someone was in a hurry to get their last words saved before being eaten.
Jargon will become common, since it lets you pack more information into 15w. Eventually, you'll have a conlang with words largely made of runes and where one word might run on for half a page.
Writing to your server "please have X scrying done" for a colleague at home to see and respond to is rather useful for a field researcher. This can extend to banks cross-checking about money being withdrawn in multiple places, coordinating the lab's Hogswatch party, or many other things. Depending on how formal/public it is, this will look more or less like the library.
Espionage gets benefits here, and a spy will often get basic arcane training, just enough to use this spell.
Although it becomes a bit recursive, wizards will also use this to write stories and play games with each other - postal chess is just the beginning. That will be set up according to personal taste.
The Internet had/has a reputation for indelicate, nay scandalous, uses. Eventually, one of the wizards will create a "premium charge telephone service", or equivalent. That will probably look like a "2gp for next page" or a running narrative.
A message expanding to a few choice insanity-inducing pages of the Necrotelecomnicon instead of the expected interesting article would be a tool-of-choice for some cultists, trolls, and general offensive use. What, you thought something which can inject stuff into the brain of a passing wizard would be harmless? (This is also used to detect spies.)