Ok, so I submitted a bug, but didn't even receive the automatic reply.
I'm posting here.
Solar Flare and it's variants don't seem to apply the weapon/spell buff to abilities which are non-targeted.
So ground targeted abilities, and automatically activating AoE do not get the buff.
This includes abilities Elemental Wall, Spear Shards, Fire Rune, Cleave, Jabs
I thought it was AoE, but then I checked and abilities that do splash AoE ("and x nearby take y damage"), do get the buff.
So, all targeted abilities get buffed. This includes abilities like Explosive Charge, Reflective Light.
All Single Target abilities get the buff.
Yes, I'm aware that targets hit by the flare are the only targets that take extra damage. I tested the abilities mentioned very thoroughly at the cost of many deaths.