Skype, steam and slack do not flash, beep or pop up when I get messages, they just put a discreet number on the taskbar. I've learned to ignore that number until I'm ready.
As a result, I'm always online on my chat programs but my responses can take anywhere between 30 seconds and 4 hours depending on what I'm doing. If it was really that important, people would walk over to my desk. That only happens about once a week.
My experience has been most developers and managers are fine with this.
That this may not be the most effective way of reaping the value of employing you is a different concern.
I use it sparingly to good results.
You're not a good PM if you've done this. The alternative from a good manager:
"Hello... I need you to input your time on Kimble"
What about my Skype status "async mode on" don't they understand?
On KDE, I'd use the "Filters" setting for either the Task Switcher (Alt+Tab thing) or the Task Manager (taskbar), or both. They can show or ignore windows from other virtual desktops, screens, or minimized ones. [Or "activities", but I've never used that feature, and I'm not sure what it's for.]
I usually keep Skype on my second screen, covered with other work, and have the task switcher set to only scroll through not-minimized things on the current screen.
Edit: So "Activities" are something like super-virtual desktops, and appear to be exactly for this purpose, to separate different tasks.