Why is that a Windows problem and not a Discord or Steam issue?
Well, in large part it has to do with how Windows loads libraries. For example, if you have two Electron apps running (eg. Discord and Slack), both will load separate libraries, effectively doubling their load on your system (scaling for each app you open). The solution is to enforce dynamic linking, like how Linux handles it. You can have Spotify, Discord and Slack all running on the same Electron library.
Aren't they using bundled/vendored versions? The OS can't help that; it's like Snaps on Linux.
Which still do not increase the booting time like that
It will if you set them to launch on boot/login, which is probably the real difference (Windows has a tradition of apps auto starting, *nix has less).
This has nothing to do with Windows and everything to do with Discord and Slack deciding not to use dynamic linking.
I mean, the same apps on Arch Linux don't slow me down at all. So in some ways it must be a Windows issue.
Steam doesn't slow Debian (LXDE) at all, because the desktop environment doesn't require two processor cores – even though Steam is mostly Electon-based now.
What's the advantage of having Discord installed instead of using it via browser?
It seems so odd to me to install programs that still need an internet connection anyway to work.