Yeah, I've always liked to frame what she does as Illuminate them, inspiring them to transform into a better version of themselves. We know that, like Dalinar, Shallan as a Lightweaver uses Spiritual Connection as well (Pattern confirms it in OB)¹ via her sketches, possibly Identity as well to see their ideal Spiritual selves. I've attached some relevant WoBs right below:
As for Renarin's futuresight, I like to think of it as a Resonance: Illumination of Progression
Yeah, the usage of light could indicate he finds it easier to use the fundamental components of Illumination: light
I like to think of it as how the power should behave being coded into the Surge. Lightweaving uses photons/EM wave, sound wave or waveforms, plus forming Spiritual Connection to people or things which Lightweavers use by virtue of often being artists of some sort¹, plus mnemonic abilities, their resonance².
So it could be that what Renarin is doing is using the fundamental pieces that make up the code of Lightweaving, the building blocks of the Surge of Illumination.
We do have confirmation that different Orders can manifest their Surges a bit differently³, more specifically we also have confirmation that Truthwatchers use Lightweaving a bit differently⁴:
1: from Chapter 120 The Spear That Would Not Break
2: WoBs
3: WoBs
4: WoB