I feel your pain about fishing out dropped screws.

Notice in the picture the Blue “magnetic paper holder” at far left.
This has a very small “super magnet” you see attached to the Phillips bit in the Red handled extendable screwdriver, which is less than 1/4.

Attaching the small super magnet to the long shank screwdriver set at right also greatly increases holding of screws.

You will have to search for the Blue paper holder, but similar small diameter super magnets are in other consumer objects.

Note also the silver telescoping “magnetic extendable wand” attached to the tweezer handle.