Yeah, I have been down that road too. Trying a lot of supplements for sleep, but not many that work. I think the main problem here is that I have been on drugs so long that my brains functionality and structure has changed. I read a article that the brain actually changes when on psych drugs. For example by producing very little dopamine and serotonin. Inhibiting gaba. Etceteta. And people who actually do manage to get off drugs often report it takes many months or even over a year before their brain goes back to normal.
A lot of stuff that works on a normal brain doesen’t work on a medicated brain.
I don’t know about the l-theanine study, but if they only tested it on recently diagnosed and recently medicated people it’s not representative.