I tried to make a minimal example that just downloads a URL passed as the first argument:
https://github.com/julianoes/qt-ssl-example

The output is:

./ssl-example https: //example.com Buildversion: "OpenSSL 1.1.1g  21 Apr 2020" qt.network.ssl: QSslSocket: cannot resolve EVP_PKEY_base_id qt.network.ssl: QSslSocket: cannot resolve SSL_get_peer_certificate Runversion: "OpenSSL 3.0.2 15 Mar 2022" Supports SSL: true qt.network.ssl: QSslSocket: cannot call unresolved function SSL_get_peer_certificate SSL error: The peer did not present any certificate Download of https: //example.com failed: SSL handshake failed

As I understand the workaround is to install openssl 1.1.1, however, that's not straightforward on Ubuntu 22.04. I have seen many reports of people struggling with this problem but no clear statement whether this is something that should be supported/fixed by Qt or whether it is a distribution problem and is only be fixed in Qt 6.

Sidenote: I'm asking because I'm trying to fix https downloads on a reasonable big open-source application ( https://github.com/mavlink/qgroundcontrol/). The project is still on Qt 5.15.2 as it will be a bit of an undertaking to move to Qt 6, and open source projects don't necessarily have the resources to quickly do so. But still, we would like to not break functionality for Ubuntu 22.04 which are considerable share of the users. The application is usually deployed using an AppImage but the ssl libs are not included by default.

Here is more reading that I have done on the topic:

https://github.com/kiwix/kiwix-desktop/issues/871#issuecomment-1611272912
https://github.com/probonopd/linuxdeployqt/issues/422#issuecomment-599032763
https://stackoverflow.com/questions/71997447/qt-missing-openssl-3-x-support-on-ubuntu-22-04
https://forum.qt.io/topic/136258/ssl-issues-after-upgrading-ubuntu (Qt 6)
https://forum.qt.io/topic/136960/does-qt-5-15-support-openssl-3-x
https://bugreports.qt.io/browse/QTBUG-103820