Also seem to be broke every damn monday

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.