It also creates issues for people wanting to contribute to the OCaml
manual on e.g. GitHub. It is not possible to create a pull request with
a change to the manual on any public platform because that would be
publishing without approval.
I think this view is exaggerated, as I don't think that the people who wrote this clause would consider hosting (modified) .etex files on a Github clone of the manual's repository as "distribution". To "distribute" the documentation or manual, I would at least expect a rendered (compiled) version of it. It is not necessary to distribute a rendered copy of the manual to contribute to it.
I'm not particularly fond of custom licenses either, but I don't think that they should be interpreted as making open-source contributions impossible.