Some Visa Advice

Greetings from a fellow Singaporean in Germany (my wife)!
If you cannot or don't want to get a visa based on the relationship (which means marrying or making a baby), then you must get a visa on your own merits.
Options are work, study (a full-time language class is sufficient) and a few more oscure ones like WHV, Aupair, JSV, etc.

I would wonder if you even qualify for a Job Seeker Visa since it requires not only a degree but also 5 years professional experience. If you have trouble to get it, you can still look online for jobs or come to Germany on a tourist visa and look for a job. You just can’t start the job directly without getting a work visa if you haven’t got a JSK. And for this you need to return either to your home country or country of residence. If you are still a resident of Belgium then it should be possible from there. But if you have already given up legal residency there, then you might even have to go back to Singapore to apply. In the end, it never hurts to go to the immigration authorities and see what they say. Exceptions to rules are not unheard of. When you tell them you have been living in Belgium the last few years then they can see the logic of why it would be a hardship to expect you to go to Singapore to apply.