[backport#16227 6/8] Move various SigningProviders to signingprovider.{cpp,h}

Summary:
Moves all of the various SigningProviders out of sign.{cpp,h} and
keystore.{cpp,h}. As such, keystore.{cpp,h} is also removed.

Includes and the Makefile are updated to reflect this. Includes were largely
changed using:
git grep -l "keystore.h" | xargs sed -i -e 's;keystore.h;script/signingprovider.h;g'

https://github.com/bitcoin/bitcoin/pull/16227/commits/37a79a4fccbf6cd65a933594e24e59d36e674653

Depends on D6557

Partial backport of Core PR16227

Test Plan:
In CMake build dir:

ninja check-all

In autotools build dir:

make check-recursive
./test/functional/test_runner.py

Reviewers: #bitcoin_abc, nakihito

Reviewed By: nakihito

Subscribers: nakihito

Differential Revision: https://reviews.bitcoinabc.org/D6558