Besides the previous comment, I find it fine. As your point out the (lib)semigroups patches of #40501 should go. This PR could also be merged with #40501.

would be good if this is checked on the latest macOS/XCode

On macOS 15.5, the answer is

• partially "yes": gap_packagesand libsemigroups get installed;
• partially "no": qhull and symengine do not.

More later.

this PR does not touch qhull and symengine.

also note that Semigroups is no longer installed by gap_packages, so to install it you need to ./configure --enable-semigroups followed by make

I passed a full test, two minor issues. A failed test in src/sage/rings/number_field/number_field_element_quadratic.pyx; it passes when testing only the file. And a failed test in src/doc/en/reference/spkg/semigroups.rst:

Failed example:
    libgap.LoadPackage("semigroups")       # optional - semigroups
Expected:
    true
Got:
    #I  ReadPackage could not read <digraphs>/gap/doc.g
    <BLANKLINE>
    true

Running interactive:

sage: libgap.LoadPackage("semigroups")
#I  ReadPackage could not read <digraphs>/gap/doc.g

true
sage: libgap.LoadPackage("semigroups")
true

Please see #40512.
And feel free to sort things out.

I passed a full test, two minor issues. A failed test in src/sage/rings/number_field/number_field_element_quadratic.pyx; it passes when testing only the file.

this is something unrelated, I think.

And a failed test in src/doc/en/reference/spkg/semigroups.rst:

Failed example:
    libgap.LoadPackage("semigroups")       # optional - semigroups
Expected:
    true
Got:
    #I  ReadPackage could not read <digraphs>/gap/doc.g
    <BLANKLINE>
    true

Running interactive:

sage: libgap.LoadPackage("semigroups")
#I  ReadPackage could not read <digraphs>/gap/doc.g

true
sage: libgap.LoadPackage("semigroups")
true

I cannot reproduce this, for me it just works.
This should not be different from the old setup, with semigroups GAP package built as a part of gap_packages.

care to give this a positive review?

care to give this a positive review?

Enrique gave a positive review 2 days ago, I think.
In any case, positive review from me too.

I see the same doctest failure that Enrique mentioned in his comment on 30th July:

File "src/doc/en/reference/spkg/semigroups.rst", line 15, in doc.en.reference.spkg.semigroups
Failed example:
    libgap.LoadPackage("semigroups")       # optional - semigroups
Expected:
    true
Got:
    #I  ReadPackage could not read <digraphs>/gap/doc.g
    <BLANKLINE>
    true

The file src/doc/en/reference/spkg/semigroups.rst is generated by the bootstrap script, but the doctest can be corrected in build/pkgs/semigroups/SPKG.rst (line 13ff).