1.
The online SageMath reference manual at
has a "Quick search" box in the left column.
It works, albeit with some JavaScript trouble:
which could take some love... Anyone with that skills?
2.
After installing from source or from binaries, one can also
browse the reference manual offline at
file:///path/to/sage_root/local/share/doc/sage/html/en/reference/index.html
There, the "Quick search" box does not work at all.
What would it take to make it work?