There are there are three different privileges surrounding tags, granted at different reputation levels published here.
Different Stack Exchange communities grant privileges at different levels, but currently for ServerFault they are as follows:
300 create tags - Add new tags to the site
2500 create tag synonyms - Decide which tags have the same meaning as others
5000 approve tag wiki edits - Approve edits to tag wikis made by regular users
Which means that at your 400+ reputation level you have sufficient rep to create new tags.
There is nothing immediately obvious in the manual at which reputation level you can start editing tag wiki's, but maybe that privilege is included with the edit community wiki privilege, granted at 100 points.
I think that implied in the approve tag wiki edits privilege is that edits from users with a rep below 5000 reputation need their tag wiki edits to be reviewed before they become visible.
The number of active reviewers on ServerFault is quite low (I'm no longer one of them either) so edits might be pending for quite a long time.
For instance the relatively new SLES15 tag https://serverfault.com/tags/sles15/info currently shows
Once I hit the Edit Pending button I see the review option and your suggested edit:
