The serotonin in your gut doesn’t “directly” affect the serotonin receptors in your brain, but it does directly stimulate the vagus neve which does influence serotonin receptors in the brain. The microbacteria in the gut are also responsible for metabolizing and producing tryptophan, which the brain requires to produce its own serotonin.

So it kinda depends on how you define directly. There is an ongoing debate in medicine on how artificial the delineation between the central nervous system and peripheral nervus system really is, and whether they should even be partitioned into different sub systems for educational purposes.

Doing so is kinda a artifact of the past and has led to a lot of people attempting to define the brain as some kind of computer for the body, when in reality the functionality of the brain is really inseparable from the body.