So, in the end, here is how I finally managed to do it: as the error suggests, and couple of answers also points out to, the Certification Authority's certificate chain is missing from my configuration, and is not in the pack downloaded from https://curl.haxx.se/docs/caextract.html .
So in the end, I found this question that pointed me in the right direction: I went to the website I was trying to connect to using firefox, and exported the certificate as type "X.509 Certfificate with chain (PEM)", to the file C:/Development/examples/mycert.pem . Then, I changed my php.ini configuration to
And that did the trick! I can connect to the website without issue.
It is also possible to simply copy-paste the content of my.website.com.pem at the end of the file downloaded from https://curl.haxx.se/docs/caextract.html, and it works as well, and is probably more versatile if you need to connect to other websites that are using certificates with php curl.