Now the error message is that it cannot find "mysql.h"--a file that exists nowhere on the machine

That file and the rest of the mysql library ships with Strawberry Perl 5.32.1.
The 'mysql.h' file is in Strawberry's c/include/mysql50716 folder, the static library ('libmysql.a') is in Strawberry's c/lib folder and the shared library ('libmysql__.dll) is in Strawberry's c/bin folder.

If you're using Strawberry Perl, I recommend building against that mysql library, rather than the one that xampp provided.
After all, the mysql library that ships with the Strawberry Perl distro is the one against which Strawberry's DBD::mysql was built.

OTOH, if you're using XAMPP's perl, then you should build against the mysql library that they provided.

HTH.
(I haven't read this thread thoroughly, and I don't do databases. I concede that this post might therefore be of no help at all.)

Update:
By the way, XAMPP's version of Perl is: 5.32.1, said to be "built for MSWin32-x64-multi-thread"

If you want to check that this version of perl is compatible with Strawberry Perl 5.32.1, just run perl -V:archname using your Strawberry Perl 5.32.1.
If it reports 'MSWin32-x64-multi-thread', then they're compatible. Else, they are incompatible.

Cheers,
Rob