Happy chemical glands. That is almost correct, but the mechanism is very different.
Think of it like this, specifically for SSRIs and psychedelics: Different drugs will bind to receptors in the brain that would normally be triggered by serotonin. Psilocybin, DMT, serotonin, melatonin, etc, are all basically the same "shape" as tryptamine, a precursor to most of those. The effects of different chemicals finding a place in serotonin specific receptors that have the same shape can be wildly different than serotonin.
To use a car analogy, its like putting pure ethanol in your fuel tank instead of gasoline. They are both flammable liquids that you can pour into your car as fuel, but they burn at completely different rates and can alter performance significantly.
What this does as far as serotonin is concerned, is that serotonin is more widely available to the rest of your brain. In the case of antidepressants like SSRIs, they function the same way but only bind with specific receptors and don't cause you to get high and trip. This allows serotonin to be more evenly used across the brain, in a manner of speaking.
As far as tolerance is concerned, different drugs will bind to receptors in different ways. Once you have "saturated" a receptor, it takes a while for it to be ready for another round. Psilocybin and even ketamine are being shown to be hundreds of times more potent than common SSRIs (in some ways), so it takes a while for those affected neurons to "recover". It's not that you have depleted your serotonin, it's just that natural serotonin has fewer places to bind to.
It's very important to realize this distinction. Combining SSRIs with other drugs can cause an extreme excess of serotonin in your noggin. Serotonin has no place to go so it builds up and causes a condition called serotonin syndrome. It's not a good thing and can be fatal.
My explanation absolutely does not cover all the details. However, it is just supposed to be a shift in how you think about how these chemicals work.