I like to categorize my apps. In Nova I have them divided into Web / Media / Games / Tools / System and I can swipe between each page (horizontally) of them. I use quite a few apps to do a lot of things tho, so *shrug.
I also really like the Sesame search integration, Lawnchairs adaption of Pixel Launchers is good. But there is style and behavior customization that Nova offers that Lawnchair doesn’t.
I am pretty particular about making my phone just look and behave the way I want it, of course it changes over time as phones and apps get better but yeah… It’s largely why I preferred Android from the start and have stuck with it
I replaced Nova with Kvaesitso and honestly its pretty awesome.
Its more limited than Nova was but it meets my use cases. The biggest adjustment was using labels to filter things instead of using folders, which I’ve actually come to like better.
But plenty of customizations for everything else you mentioned and more.