Random Riddle: Rather be a Tree

I also cannot move around,
Or at least, not on my own.
Unfortunately, I can make no sound,
Except perhaps a squeak.

If you chop off my head,
You are left with a hair.
If you chop off my tail,
Only tea is left there.

One more clue I will add,
Is that you often use me.
Yet you barely ever notice,
In fact, I’d much rather be a tree.