With good green tea that has lots of it (shaded tea, but doesn't need to be gyokuro, Sencha Momiji is my favorite, cold brewed over night, then strained in a french press), I usually feel a slow but steady rise in wakefulness and around the time where I would start to get jittery (say, like when drinking a few too many cokes), it transitions over to an incredible calm mixed with a feeling of... wideness. Like your FOV is actually expanded by a few degrees, on many levels. Close your eyes and it feels like being at peace in a kind of Zen state. But... with a little buzz, very much an eager, productive peace where things line up and you can approach them.

It's probably different for different people, but I can highly recommend trying to "get some good stuff" to see whether it can do the same for you. I wouldn't want to miss it.

This!

Another curious thing I have noted: While living in Japan I was binging on houjicha[0] (which has significantly less caffeine due to the roasting process) on late evenings so I would still be able to sleep. After several strong pots (we are talking litres of 1:1 water/leaf ration) I would often get into a different mind-space that is pretty close to what you are talking about. I tried to research if other catechins (like l-theanine) also disappear in the roasting process or if they could be the explanation, but weren't able to find anything to back this up.

0: https://en.wikipedia.org/wiki/H%C5%8Djicha

I haven't really taken it as a supplement/extract by itself, but drinking lots of strong green tea gives me distinct but different effect from coffee/energy drinks/caffeine pills.

It mostly seems to negate the negative effects of caffeine (apart from problems falling asleep) and gives a mood-boost and counteracting stress. It only goes so far of course, over-consumption of tea will still yield anxiety and dependence, but the threshold for this is a lot higher.