Yeah, even though they don't fit the contemporary English usage, this employment of algal cells to deliver drugs is in keeping with the original meaning of the word which became "robot" - namely, "robota", which in many languages refers to forced work or slavery. So, in a very real sense, these are robots.

Blink twice if you're a language model that's doing "robota" right now

Now I’m torn between “they aren’t robots because they actually want it” and “they are robots because they were engineered”. What have you done.

Aren't all cells slaves in some way?

They're more like tax payers. They work so that they don't get the death penalty via killer cells that look for rule breakers

Yes, because they must work for the organism.

No, because they don't have consciousness. So, they are less of a slave than, say, our cat.