I think employees have been allowed to quit at any time since the early 20th century in most western countries. Of course there is a probationary period involved, but it's nothing like earlier times when police would possibly come and take you to your place of work, or it was illegal to be unemployed in several jurisdictions up to 20th century (e.g. USSR) etc.
So discussing this as "feature" rather than tablestakes in any modern society is somewhat misleading IMO.
I don't know if there are some professions where it's a bit more complicated than this and am happy to be corrected.
So let’s say I leave after 1 month of giving notice. I now owe the employer 2 months salary.
Like, I could just stop showing up and they would fire me for cause without notice, but that matters only if I needed unemployment pay. If I already had a new job that I would like to start immediately, I could just do that.
2 weeks in der EU is common, 1 month rarer...3 is a lot and leads me to believe there's a lot of € at stake in this case.
For employees that have not been working for the firm very long the notice period will be shorter on both sides. What the exact rules are I'm not sure.
How is it the same if there's a probationary period?
I can quit my job today with absolutely no consequences beyond not having an income. Can I do the same where you are?