I'd suggest no because it affects "abilities" with a cast time or channel and basic attacks are probably not considered an ability.
I'd also suggest it's only worth it with swords on one bar usIng would shine swords as it permits using 2 - 5 PC sets and monster set. Probably the only class that can pull that off and get decent use of the soulshine will be a Templar with jabs and RO.
Puncturing sweeps
Jesus Beam
Lightning heavy attack
Dark Flare
Rite of Passage
Proximity Detonation(sometimes)
those are the attacks/skills i tested myself.(Combat Metrics)
Note that it gets increased by major and minor sorcery though it is never shown in any tooltip
Second note: It is quite buggy sometimes the 5 pc bonus tends to stay or functions on Abilities i would not expect.
It boosts fire, frost, and shock staff heavy attacks
Fully charged heavy attacks are considered a cast time by the game
Lighting staff heavy attacks are also buff by Thamaturge
So staff expert, elemental expert, and thuan all buff lighting staff heavtmy attack damage.
Rinaldo Gandolphi-Breton Sorcerer Daggerfall Covenant
Juste Gandolphi Dark Elf Templar Daggerfall Covenant
Richter Gandolphi - Dark Elf Dragonknight Daggerfall Covenant
Mathias Gandolphi - Breton Nightblade Daggerfall Covenant
RinaldoGandolphi - High Elf Sorcerer Aldmeri Dominion
Officer Fire and Ice
Co-GM - MVP
Sorcerer's - The ONLY class in the game that is punished for using its class defining skill (Bolt Escape)
"Here in his shrine, that they have forgotten. Here do we toil, that we might remember. By night we reclaim, what by day was stolen. Far from ourselves, he grows ever near to us. Our eyes once were blinded, now through him do we see. Our hands once were idle, now through them does he speak. And when the world shall listen, and when the world shall see, and when the world remembers, that world will cease to be. - Miraak