Has anyone ever actually commented to you on "hey you weren't around earlier and it was a problem?" You should ask yourself this first.
Second, are these interactions with people who share a messenger/interoffice communicator? Most places have something you can set a status to "away" or "be right back" which is considerably more professional in my opinion.
Assuming you have people asking and cannot use this, to answer
Firstly, is it even professional to leave stickies? It feels childish
This depends completely on your office environment. Some places this would be seen as completely unprofessional and some places this is completely fine. Because you are asking about this, it would seem you have a slightly more professional environment, and if you really do not think a post-it/sticky would appear unprofessional, simply print off a page saying "Sorry I missed you - I am away" or something similar. Or if you have a whiteboard at your desk use this. Lots of more professional options.
Secondly, also I have the nagging feeling of being mistaken. What if
I'm mistaken to be a slacker who takes breaks that are long enough to
justify writing a note, by someone like say my manager? What is the
popular approach here?
Again, this completely depends on the environment. If your office is a 7:00 - 11:30, lunch, 12:00-3:30 type of office where you have a very structured working hours you may be seen that way. If you work in a more laid back environment then not.
Having a printed sheet, by the way, would make this seem less "slackerish" if you use the same sheet every time.
Something else to keep in mind is you may be making a huge issue out of nothing. People in office environments are frequently gone for meetings or other obligations other than breaks. This is to be expected in most environments. Additionally, as people become management or have more responsibilities, they even more often away from their desk.