I use it mostly for sleep 100-150mg in combination of 5HTP which I found it to be an incredible sleep cocktail. I generally don't have trouble sleeping but this cocktail gives me great dreams and increase the quality of my sleep where 6-7 hours is very much enough for me compared to the usual 8-9. Unsurprisingly, l-theanine is popular in lucid dreaming communities and while I have no particular interest lucid dreaming my dreams are definitely more vivid and most importantly instantly forgettable (like normal dreams are) which is the most desirable outcome imo.
250+mg does have my mind racing a bit and this dose will prevent me from falling asleep effectively (at body weight of 75kg), anything above 200mg seems too much imo for my body weight. So I think the effect is very much observable just through dose variability.
For day use I've tried l-theanine with caffeine in the morning and I'd say the effect is similar to mild adhd medication (I've been told it compares to like ~2mg of Ritallin or pinch of Kratom powder). Tho for me it always comes with side effects similar to a cup of too much coffee would have. I found that just like adhd medicine, it works best with a protein shake.
This is my unscientific anecdote, tho OP's post makes me want to record my own experiences.