Serotonin produced in the gut doesn’t get into your brain.

This factoid is repeated everywhere but it’s misleading without knowing that gut serotonin is a different pool than brain serotonin and they have different functions.

The brain synthesizes its serotonin locally within the brain.

The blood brain barrier is a deny by default firewall. If there is no transporter configured for a particular molecule, it doesn't get through. There is no transporter for serotonin