Having an assembly does not mean you have democracy.
“I want to note this up front because it is important to recognize that the existence of a popular assembly does not make a Greek polis a democracy, nor does the existence of a powerful magistrate make it a tyranny. As we’ll see, Sparta has an assembly, it is just laughably weak; it also has two very powerful magistrates, but their power is strongly checked. What matters is the division of power between these parts. I also wanted to start here because Sparta follows this basic model, but with some interesting variations. Knowing what the normal model looks like will make it easier to spot the variations that are unique to Sparta.”
https://acoup.blog/2019/09/12/collections-this-isnt-sparta-part-v-spartan-government/