Black tea and green tea, like Earl Gray or Matcha, yes they have caffeine.
Chamomile or tea of an other non-caffeinated plant boiled in water, no.
After that, I slept much better. I could finally fall asleep, it wouldn't take me an hour to nod off. I stayed asleep, I wasn't getting up 2-3 times a night. My anxiety, which I then found out contributed to my sleep problems, that pretty much went away. I used to plan and replan scenarios in my head, come up with pithy quips to conversations that would never happen, fear saying or doing the wrong thing in imaginary conundrums.
It all just disappeared after I quit caffeine. I felt 'normal' for the first time in decades. I woke up having the best night of sleep in my memory. And then it happened the next morning, and the next.
Currently, I don;t sleep all that well, but a new baby is the culprit. I can't imagine having a newborn and being on caffeine again, my anxiety would spiral out of control. I'd be a mess for my kid, projecting things, being a jerk.
One of the best little random challenges I ever gave myself.
I gave up caffeine on a lark during lockdowns. Man, great decision. I've never slept better and my anxiety went way down too. I'd had no idea what that stimulant happened to be doing to my system.
I had been tapering down my caffeine consumption too, but going cold turkey had a major difference for me.
I'll caution that 3 days of pretty intense headaches were the cost, but for me, the benefits were immense.
I still go through a coffee ritual-thingy in the mornings with teas, so that is still nice to have.
Others in my family have tried this, but saw no real benefits, so went back on coffee. Your mileage may vary too. Still, I think it's worth a shot if you're having sleeping issues.