I am aware that JS has >> apparently for signed-numbers shifts and >>> for unsigned.

I tested two simple examples in the node console:

a = 0b10000000000000000000000000000100
> a >> 31
-1
> a >>> 31
1

I've read mdn, w3schools, etc. But I expect both cases to be 1.

Also, see a 31 bit number:

a = 0b1000000000000000000000000000010;
a>>30
1 
a>>>30
1

What is the mistake?

May be related to JS reading the number as 32Bits, and using that last bit as a sign?

> (a & a).toString(2)
'-1111111111111111111111111111100'