This new option is similar to --all but

• it tests all Sage modules installed (in SAGE_LIB) instead of SAGE_SRC. (This will be useful for testing modularized distributions such as Modularization of sagelib: Break out a separate package sagemath-standard-no-symbolics #32601.)
• it tests the installed Sage documentation (specifically, the .rst.txt files installed in html/**/_sources) instead of SAGE_DOC_SRC.

$ ./sage -tp --installed
too many failed tests, not using stored timings
Running doctests with ID 2022-02-23-21-52-47-11831639.
Using --optional=ccache,cryptominisat,debugpy,e_antic,homebrew,igraph,jupymake,lrslib,normaliz,pip,polytopes_db_4d,pycryptosat,pynormaliz,sage,sage_spkg
Features to be detected: [...] 
Doctesting all installed modules of the Sage library.
Sorting sources by runtime so that slower doctests are run first....
Doctesting 3522 files using 8 threads.
sage -t --random-seed=334799075370772165291245032923424842623 local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/groups/matrix_gps/heisenberg.py
    [32 tests, 1.83 s]
sage -t --random-seed=334799075370772165291245032923424842623 local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/combinat/crystals/alcove_path.py
    [293 tests, 4.16 s]
...

(Actually, because portions of namespace packages can be installed in separate locations, the variable sage.env.SAGE_LIB is no longer meaningful. Instead, we make use of the __path__ attribute of packages, https://python.readthedocs.io/en/stable/reference/import.html#module-path, which in the case of namespace packages is an iterable.)

This would also make sense for distribution packaging, which no longer would have to rely on the fallbacks SAGE_SRC -> SAGE_LIB and SAGE_DOC_SRC -> SAGE_DOC.

Part of Meta-ticket #33037.

CC: @kiwifb @antonio-rojas @tobiasdiez

Component: doctest framework

Author: Matthias Koeppe

Branch/Commit: b4d2b8e

Reviewer: François Bissey, Antonio Rojas

Issue created by migration from https://trac.sagemath.org/ticket/33407