Improve multi-monitor experience/support

[emmegamma]

I have a laptop that I sometimes connect to external monitors.
Unfortunately, I noticed that Mint/Cinnamon has some long-term issues that have been around in Linux for long, and the experience was overall quite poor. In chronological order:

1. When booting, Plymouth is only showed on the main (laptop's) one. That's surely not very important and might even be okay, if it was a consistent choice. However, after booting comes the login and..
2. LightDM is shown on all monitors. But it is apparently unable to manage different resolutions: when I connected one monitor, the login screen was duplicated on it, but half of my laptop's screen was black, with LightDM shown only in a corner, probably because of the high resolution (laptop: 2880x1800, monitor 1920x1080).
   Then, to add inconsistency: when connected to two external monitors (through a docking station), the login screen was duplicated on one, while the other monitor showed only the background image.
   Still, login was possible, so that's okay, but then..
3. The experience after logging in was quite messy: the panel cannot be duplicated on other monitors. and though it can be added manually, applets do not inherit the configuration, so any customization must be reproduced (and updated, if something changes). Also, scary behaviors can happen: while trying to find the best configuration, I set the external monitor as primary, and then moved the panel to the secondary (laptop's) one, without really realizing what I was doing (I thought "I want my panel where it's habitual, but new windows to open on the external monitor). Then, when disconnecting the monitor, the panel disappeared from the laptop to be replaced with a plain, unconfigured one (or worse with no panel at all: whatever was on the external monitor, the "primary", is retained): so I found myself without a panel or with a non-ideal configuration, and needing to reconnect the external monitor to recover my main panel.

I understand now what my role was, but the overall experience, I must say, was quite poor.

I know this is not all on Linux Mint/Cinnamon's devs, there's parts related to external projects (LightDM), and I know it can be quite a lot of work, but... I think it's really an important feature in 2025.
As a user, I would likely just be able to connect an external monitor and start working. Ideally, I guess one would like to have the login screen shown only on one monitor (background extended to the second one), and then when logged in a simple option to either display the panel on other monitors or only on the primary one. I started looking into JS and I understand in practice it may not be a simple task (what to do with all the applets'?), but that's what I'd want as a user.
There's also other reports on this very website that go in a similar direction, though more specific: #286 and #630 on taskbar and applets, and #272 on OSDs

But again, I think it would be really nice to work on the overall experienceIt's something where all DEs are seemingly lagging behind (at least GNOME, where the panel can't be moved or replicated: though I appreciate the choice in that it avoids troubles) with respect to Windows or Mac, and so where users might be pulled back.