I added the line for TLS v1.0 and set all TLSs to 1. Now mail sending works again!

Awesome!

which looks like a very bad setting.

When a setting isn't present, it causes Opera to use the default value for that setting. In the case of v1.0, that should be 1. You can remove all the settings from the file to have Opera use the defaults and see if things still work. When the settings are present, that usually means the user set them (unless of course Opera added them as an override in a past update).

The default settings in the latest build should be v3=0, v1.0=1, v1.1=1 and v1.2=1. But, in the past 1.1 and 1.2 were off and v3 might have been on. 1.1 and 1.2 were off as they caused problems. v3 should be off now as it's insecure.

Since 1.0 was already defaulting to 1, it sounds like the server needed 1.1 or higher or at least had some problem negotiating down to 1.0. Or, it was something else.

Glad you got it working.