How do I do it so that when I place the pointer over a category (accessories, internet, etc.) it immediately appears on the right like in Windows?
Unfortunately this can't be set only for that. The best thing I can think about is the click assistant feature on accessibility settings which can be helpful for this but of course is applied everywhere.
Yes, using a different Menu Extension is the only way I know of. In using Lite, I used WhiskerMenu and it does exactly as the O.P. requests.
Try Arc menu, it may do or can be set up to do that. I can't say for sure as I'm using Plasma/KDE DE. But have a look
https://extensions.gnome.org/extension/3628/arcmenu/
requires: Browser gnome extension (install in browser) and Gnome extension app (softwarecenter)