Please do not post the same question twice. Please delete the content of the message in the other thread with an appropriate note.
To your question:
I would be surprised if there were no browser add-on for this feature. Another possibility would be e.g.
https://autohotkey.com/ with which a regular <F5> can send to the browser if (and only if) the corresponding page is open. In addition, with AutoHotkey the page can be brought to the foreground (and much more).
With JavaScript you can certainly program that too.
Perhaps the DokuWiki ~~NOCACHE~~ option is also helpful for the page in question.
HTH - Michael Sy.