Could you please make a method to actually set timeout in WiFiClientSecureCtx?

You are hard coding the timeout, which overrides the setTimeout method, so in this case setTimeout has no effect.

It sometimes overrides with 5000 ms, and for the first TLS and SSL handshakes, it's 15000 ms, which is too much in so many cases, especially when the esp is connected to a poor network.The ESP goes blind for 15 seconds with every secure request.

You could instead implement a method that checks if the user set a timeout so it respects it and uses it instead of hard-coded ones, If the user didn't set the timeout, you can use your hard-coded timeouts.