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I haven't looked too deep into what's possible with the config files of i3 or awesome. Maybe I should do that first. I just assumed they would be too keyboard focused. I want everything to be visible on screen, so you don't have to remember hotkeys.
What you want should be quite easy to achieve with i3/sway or awesomewm. i3 has a slew of possibilities for "bars", even the xfce/kde panels: https://wiki.archlinux.org/title/i3#i3bar_alternatives
Awesomewm is totally usable via the mouse and infinetly extendaple via lua.
I just wish it would be easier to set it up and run it a s a floating WM, with proper window decorations and movement.
Why would you want it floating if every window is maximized? These requirements contradict each other.
The linux community is IMHO a bit focused on tiling WMs. I like tiling as well, but in this case: the vanilla gnome workflow is kinda 70% of what you want already. The rest can be done via extensions.
This should be possible to build with sway (and presumably any other tiling wm). Now that I'm thinking about it, you can probably also do this with gnome and a couple of extensions.
The status bar can be achieved with waybar in sway, which can be easily configured the way you described. In gnome there is an extension to rearrange the top panel.
I'm thinking of opening each window in a new workspace, can be configured for sway and gnome has an extension for that.
For the tabs we can use waybar with sworkstyle for each wroskpace, requires some configuration. For gnome I'd just use one of the many task bar extensions.
I can't immediately think of a solution for the searchable list, but I'd be surprised if it didn't exist for both systems.
Since tiling is not wanted, I think gnome + extensions should be the way to go.
That's something you can do with most window managers, but if you want to write your own wm, you can use DWM as a start.