We revise the CI workflows for Cygwin, now going through SAGE_ROOT/tox.ini for the package installation and invoking the new system package scripts from there.

We also add more stages to make the workflow more robust; this was originally done in #29152.

We also make another improvement that was easy to do:
The build now uses SAGE_LOCAL=/opt/sage-$COMMIT instead of /sage/local.
This will make it easier to download and install several versions of Sage.

Depends on #29124
Depends on #30944
Depends on #31062
Depends on #31084

CC: @seblabbe @kliem @antonio-rojas @embray @slel

Component: porting: Cygwin

Author: Matthias Koeppe

Branch/Commit: 42f4458

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/31064