I ran a test by running WordPress on the server via Docker and testing the same site that's having issues.
In wp-toolkit, which uses PHP compiled from the panel with curl 7.74.0, OpenSSL/1.1.1o continues to cause the issue.
In Docker/WordPress with curl 7.88.1, OpenSSL/3.0.14 worked perfectly.
I believe the aaPanel PHP installation needs to be fixed because it's pulling in these outdated modules.