.... so I'll have another crack at it tomorrow ....

In GMPz.xs, in the bottom section of the file I have replaced:

SV *
overload_add_eq (a, b, third)
    SV *    a
    SV *    b
    SV *    third
CODE:
  RETVAL = overload_add_eq (aTHX_ a, b, third);
OUTPUT:  RETVAL
[download]

with

void
overload_add_eq (a, b, third)
    SV *    a
    SV *    b
    SV *    third
        CODE:
        overload_add_eq (aTHX_ a, b, third);
        XSRETURN_EMPTY; /* return empty stack */
[download]

And in the top section of the file I have replaced:

SV * overload_add_eq(pTHX_ SV * a, SV * b, SV * third) {
    /* lengthy code  snipped */
}
[download]

with

void overload_add_eq(pTHX_ SV * a, SV * b, SV * third) {
     PERL_UNUSED_ARG(third); /* UPDATE: This line can be removed as ir
+relevant */
     mpz_add_ui(*(INT2PTR(mpz_t *, SvIVX(SvRV(a)))), *(INT2PTR(mpz_t *
+, SvIVX(SvRV(a)))), SvUV(b));
}
[download]

This means that we're always adding SvUV(b) to a, irrrespective of what b actually is.
This is good enough for demonstration purposes if we make sure that the second arg (b) is an IV, but we probably don't want to run make test.

On Windows 11, perl-5.38.0, I then run perl Makefile.PL, followed by make.
The build emits no warnings.
Then:

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++;print $x; $x += 15; print $x; Dump($x);"
1235
Use of uninitialized value $x in print at -e line 1.

SV = PVIV(0x1abd93865e0) at 0x1abdad3ae48
  REFCNT = 1
  FLAGS = ()
  IV = 1837594613288
  PV = 0
[download]

As you can see from that, the Math::GMPz object ($x) has been well and truly clobbered by the '+=' overloading.
Anyone interested can try this out by making the above alterations to GMPz.xs in https://cpan.metacpan.org/authors/id/S/SI/SISYPHUS/Math-GMPz-0.61.tar.gz.
Thoughts, observations, opinions and revelations are all most welcome.

UPDATE: I see the same behaviour on Cygwin, and also on Ubuntu-22.04.4-LTS.

UPDATE 2: I'll also point out that this altered version of overload_add_eq() works as expected when called as a function:

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++; print $x; Math::GMPz::overload_add_eq($x, 15, 0); print $x
+;"
1235
1250
[download]

UPDATE 3: Also, if I remove the '+=' overloading (by commenting out the appropriate line in GMPz.pm), then the '+=' overloading (which then uses the '+' overloading) works fine:

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++;print $x; $x += 15; print $x; Dump($x);"
1235
1250
SV = IV(0x2bfffa61b78) at 0x2bfffa61b88
  REFCNT = 1
  FLAGS = (ROK)
  RV = 0x2bfff38aac8
  SV = PVMG(0x2bfffa24a58) at 0x2bfff38aac8
    REFCNT = 1
    FLAGS = (OBJECT,IOK,READONLY,pIOK)
    IV = 3023652457216
    NV = 0
    PV = 0
    STASH = 0x2bfffa5e5e8       "Math::GMPz"
[download]

Cheers,
Rob

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