[3.12] gh-87891: Add ABI check to CI (#104793)

Backport the workflow change and fix-ups:
- GH-92442 (e89c01eac7731d7cb54d43252dbc3d3f3a040c53)
- GH-94129 (0dadb2249a8bafa7c5877daa08c9452f2248958a)
- GH-98556 (194588decc05fa12f04cd90c3b78cc081151b19e)

Co-Authored-By: sterliakov <50529348+sterliakov@users.noreply.github.com>
Co-authored-by: Hugo van Kemenade <hugovk@users.noreply.github.com>
Co-authored-by: Pablo Galindo Salgado <Pablogsal@gmail.com>