[...] https://meta.wikimedia.org/wiki/Special:CentralAuth/Drytime%$1600 gives Error 400400 Bad Request nginx/1.13.6
I don't know what Logstash might have kept for the error as I don't have access to it. Either what it causes the error there or we revert the rename and blacklist those weird characters. Your call :)
The CentralAuth link works with &target= parameter though. See https://meta.wikimedia.org/w/index.php?title=Special%3ACentralAuth&target=Drytime%25%241600
If the $ and % characters are converted, the page https://meta.wikimedia.org/wiki/Special:CentralAuth/Drytime%25%241600 also works well.
I think this is normal and correct. That is a bad request; the '%' should be URI-encoded to '%25'.
You can reproduce the 400 much more easily, with a '%' followed by anything other than 0-9, A-F and a-f, for example: https://en.wikipedia.org/wiki/%Z
I get the same results on my local testing wiki, with the server running Apache/2.4.18.
(Changing projects, this error is generated by the server software before it even reaches MediaWiki.)
If the incorrect "Special:CentralAuth/" link is generated by the software somewhere, that's a bug, but it seems that you manually constructed it.