The SA entry specifically refers to SCAG, but the document itself also refers to Tasha's."Introduced in the Sword Coast Adventurer’s Guide, the green-flame blade and booming blade spells pose a number of questions, because they each do something unusual: require you to make a melee attack with a weapon as part of the spell’s casting."
Was this Sage Advice written under the old version or the new version of the spell? Because I've been convinced by blue's arguments that that is no longer how the spell works with the new wording.
My original nit-picking arose because I wasn't looking at the entirety of the changes in the spell's wording, but was carrying over some of the intent of the original wording that is totally absent in the new version.
The original version says that you make the melee attack as part of casting the spell. Which sounds like it might be a Somatic component...except that version of the spell had no Somatic components, only Verbal and Material.
The new version switches the Verbal component for a Somatic component. But now it no longer says that the melee attack is part of casting the spell. Instead, it lists brandishing the weapon and making an attack as the first line of the spell's effect. The overall context persuades me that the Somatic component (which like in most spells, is not specifically described) is being separated from the weapon attack, which takes place afterwards as part of the effect of the spell.
I've found it extremely difficult to explain the particular nuance I've been attempting to address, but this does solve it. Essentially, the idea is that the PHB rules say that the free hand for your Somatic and the free hand for your Material can be the same free hand, but I have a hard time seeing a hand that is currently making a weapon attack being "free". I mean, that's kind of the poster child for a hand not being free! So even if a spell granted you the ability to make a weapon attack with its Material component, if the hand was not considered free while making that attack, the PHB would not provide permission for it to be the free hand needed for a Somatic component, and therefore you would need your other hand for the Somatic component. Since the new wording completely changes the spell though, at the time you are casting the spell the hand with the weapon is free, so it can handle both the Material and Somatic components, and then once the spell is cast, it no longer matters that the hand is occupied chopping up a monster, because the Somatic component has already taken place.
It's not clear to me if this means that the GFB clarification is intended to also apply to Tasha's version of the spell, or just to the original one, but my opinion is that the SA clarified the intent of the original wording, and the new wording is an attempt at making that intent clearer as new RAW.
Regarding the S/M component, "free" to me is not meant in an absolute way, rather in a relative way as "free from anything not related to the casting of the spell". Otherwise, you would get to paradoxical situations, e.g.: if you already have the M component of the spell in hand before you decide to cast the corresponding spell, that hand is clearly not free, so it cannot be used to handle the M component.