Crude and untested (written directly in GitHub editor) attempt to fix the mouse property::screen

fix_mouse_screen.lua

-- Instructions:
--   1) Put this into a file called fix_mouse_screen.lua in ~/.config/awesome
--   2) add require("fix_mouse_screen") to rc.lua

local placement = require("awful.placement")
local wibox     = require("wibox")

local cur = mouse.screen

client.connect_signal("focus", function(c)
    if cur ~= c.screen then
        cur = c.screen
        mouse.emit_signal("property::screen", cur)
    end
end)

awful.screen.connect_for_each_screen(function(s)
    local w = wibox {
        visible = true,
        below   = true,
        type    = "desktop"
        x       = s.geometry.x,
        y       = s.geometry.y,
        --TODO set the shape to `function() end`
        --TODO set the input shape to `gears.shape.rectangle`
    }
    
    placement.maximize(w)
    
    w:connect_signal("mouse::enter", function()
        if w.screen ~= cur then
            cur = w.screen
            mouse.emit_signal("property::screen", cur)
        end
    end)
end)