plasma-applet-tiledmenu VS Kvantum

I think there are already Plasma menus that do almost the thing you want. For example https://store.kde.org/p/1160672, https://store.kde.org/p/1367167 or https://store.kde.org/p/1367178 . Maybe it would just be better contributing to those instead of starting completely from scratch. But in the end you decide.

"tiled menu" from the KDE plasmoid shop or from here

If you want something just like the Windows 10 start menu, you may want to consider the Tiled Menu widget.

I would use the Tiled Menu plasmoid, as busy_biting suggested. It's highly configurable, though a bit clunky in some edge cases. Very functional and good looking, however! I'm not going for a Windows 10 look at all and yet it's what I stick with because of how great tiles can be.

Tiled Menu, the launcher that did tiles better than what Windows 10 did.

https://store.kde.org/p/1160672/ Tiled menu is good one

On Plasma you can download the tiled menu which has on option that makes it full-screen

I'm using Kvantum engine with my custom Andromeda theme

I think Kvantum has support for theming both Qt6 and Qt5 apps now though so that might be worth trying if it bothers you that much.

The ones I know of are: Aurorae (built-in one), Kvantum (https://github.com/tsujan/Kvantum/tree/master/Kvantum) and Lightly (just a theme https://github.com/Luwx/Lightly). store.kde.org is down (at least I can't access it at the moment), so I've shared github links.

What about : https://github.com/tsujan/Kvantum ?

Make sure Kvantum is selected in the application style section of your look and feel settings. Read through the usage instructions on the Kvantum GitHub page.

Perhaps you can submit an issue

As for Kvantum, you'll need to either install it from your distro's repos if you're lucky, or if not you'll need to compile it yourself, you can check how to do that here.

arc-theme with kvantum look petty good imo.

It's written in QT, so you need a QT theme. There's the KvLibadwaita style for the Kvantum theme engine.