I'm honestly not 100% sure, but I don't think so. Waybar does though, with the tooltip option.

Waybar is similar to Polybar, but only works on Wayland rather than X11. Configuration is a bit different, but similar in many respects. If you're using i3 with Polybar now, you can install Sway as the window manager and drop your i3 config into ~/.config/sway/, it should work exactly the same as i3 after a few minor tweaks. Once Sway is set up, you can install and configure Waybar. The config file is not a drop-in replacement like Sway was for i3, but if you can figure out Polybar, you can figure out Waybar.

Link to the Waybar wiki on Github

Sadly no. (You can prolly create drop down menu in a hacky way by creating some script that would launch a drop down looking menu and have your wm's window rules display it under the module when clicked)

Btw waybar supports tooltips(hover text thingy) but its wayland only