There are a couple of possible reasons that I think easily clear the suspension of disbelief in space opera bar. For instance:
Brains Have Been Very Extensively Field Tested
Brains have been around for at least 550 million years on Earth (and maybe far longer on some other worlds in your universe). Even if your world has developed superhuman AI, it is certainly believable that research has not managed to replicate every trick that is implemented in the vertebrate brain. As a consequence, you could for instance posit that superhuman AIs in your world are, for all their greatness, still vulnerable to variants of adversarial examples. This could mean that human labour is very desirable for jobs that do not require superhuman intelligence but which do require commonsense reasoning robust against adversarially controlled input.
For instance, say your empire is strip mining some planets under its control for valuable rare minerals in order to meet its quarterly Death Star production targets. It would be very unfortunate if rebels or environmental activists managed to make your strip mining robots misclassify improvised explosive devices as chunks of valuable ore. However, if you hire a human, your operation gains an additional layer of spoofing security and your dominion over the galaxy is assured!
Note that in that kind of setting, AIs may find it useful to optimize biological brains and bodies in such ways as maximize their ability to take advantage of specific biological capabilities while minimizing creation and upkeep costs. In that sense, the degree to which your workers end up being recognizably human may vary.
History Shows That Developing AI Is Not A Good Idea
If your setting has FTL travel, the ruins of ancient civilizations that did not successfully pass some existential risk filter may serve as reminders that the future is uncertain and that it is often unwise to overstep one's station. For instance, in the spirit of Alastair Reynold's Revelation Space series, it may turn out that some Elder Civilization is for some reason destroying everyone who develops general artificial intelligence. In such a setting, some civilizations (or enterprises) may continually test out the boundaries, but humans (and maybe aliens) would stay gainfully employed for as long as the Elders remained active.
Humans Are Competitive for Low-Skilled Labour
It might simply be that it is difficult to improve very much upon the price-performance ratio of humans for some types of relatively unskilled work (i.e. work that does not require superhuman intelligence), especially given that humans will reproduce and raise more humans for free. In that setting, your galactic empire will entrust highly complex technical work to AIs (say, the design of secure battle station exhaust ports), but simply has no reason to completely automatize the myriad of menial tasks that have always been done by manual labour and that can be executed satisfactorily in that way (for instance, the planet-side part of mining operations on planets not yet uninhabitable).