Answer: There are so many hundreds of succulents that it's hard to identify exactly what you have. From your description of the plant as a "bloomed rose" it sounds like a succulent that often reproduces by small offsets, or "pups." (The common "chicks & hens" might be a similar plant that you're familiar with.) But since no offsets have appeared, you might want to try propagating from one of the "petal" cuttings or the seeds. I like your description of the "teeny tiny bread yeast particles." After flowering, seeds are created, and as some seeds are quite small, those particles are probably the seeds!
Try germinating the seeds in both a soilless seed-starting mix, and in a cactus soil mix, to see if one works better than the other. A rule of thumb is to bury the seeds 2 or 3 times their diameter. Since these are so small, just barely cover them. Some seeds only germinate in the presence of light, so try some on top of the soil. You may have to experiment a little to find out what works best. Try some cuttings in both soil mixes also.
And finally, all cacti are considered succulents, but not all succulents are cacti! For example, an agave is a succulent, but it's not a cactus. Cacti have a plant part called an "areole" where the spines emerge. Succulents have modified stems, roots, or leaves to store moisture. I hope this helps--good luck with propagating your succulent. That flower sounds beautiful!
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