Did I make a mistake in my career planning in that the only title that is worth carrying (until full tenure, I guess) I can’t carry without a large number of not-so-fancy accessories?
No. You make the good old German mistake of thinking that ‘carrying’ the title has any relevance whatsoever. You will have the equivalent of a doctoral degree from a respectable university (presumably) backed with a reasonable publication record. This is what’s going to matter. Whether it will be called a doctorate or a PhD does not matter to any employer (that you would actually want to work for). Also, for practical purposes, the people that care about such things will be calling you Dr. Hans Wurst anyway, even if you technically have a slightly different title. It’s close enough.
The default format for PhDs from a non-EU country is something like “Hans Wurst (Doutorado, Universidade de Ipanema)”, which looks like I should just use my self-confidence instead and not mention that I did a PhD unless someone asks.
I don’t quite understand. You don’t want to mention your PhD because of ... what exactly?
I’m also wondering whether the international community is as strict as German law, or whether I should just call myself “Hans Wurst, PhD” on job applications, my professional webpage, etc. (where the place will be listed somewhere), and hope nobody tells me it should be “Hans Wurst (Doutorado, Universidade de Ipanema)” instead.
Practically, on anything but the most formal documents, I have seen people in similar situations call themselves anything out of: Dr. Hans Wurst; Hans Wurst, PhD; or Hans Wurst, PhD (Universidade de Ipanema). All of those mean essentially the same thing to the pragmatic observer.
First off, I am not German myself, but Austrian with strong ties to Germany (and Austria is the place that Germans make fun of because we are presumably so fond of our academic titles), so I do think I am able to comment on this issue.
Second, I think it is required to distinguish a few things which are somewhat mangled up in my above response as well as the questions:
Will the OP formally be allowed to carry the title Dr. Hans Wurst?
No, not without going through nostrification, as indicated in other answers.
Will people informally still refer to him as they would to the holder of a European PhD? (e.g., put a Dr. Hans Wurst on his door in the office?). Basically, would people in their day-to-day life consider the difference to be a technicality?
Yes, I am convinced that would be the case in most places. If non-EU people were treated as “not really doctors at all”, we would not have any foreign faculty or postdocs. In Vienna, while I did my postdoc there, we had people who had received PhDs from Austria, Germany, the US, and China, and they all were uniformly referred to as “Drs.” by peers and university administration alike. It may not be formally correct, but people are also not stupid (in general).
Will it make a difference in his professional life?
Assuming the university is indeed excellent (I have personally never heard of it, but my knowledge of African universities is very limited), it should really not make a difference. I guess the main problem is that if the university is not very well-known, a hiring committee might not go through the trouble of actually finding out whether or not the university is good. However, at least in academic posts, I would not assume that the OP will have any disadvantage in comparison to a holder of a German PhD. International experience is usually considered a big plus. The examples provided by aeismail and Nate Eldredge are completely opposed to every personal experience I’ve ever had.