dnd 5e – Can I use the Illusionist’s Bracers and the Twinned Spell metamagic to cast a twinned Booming Blade as both an action and a bonus action?

The only general limitation on metamagic, as stated in PHB, is:

You can use only one Metamagic option on a spell when you cast it, unless otherwise noted.

But there is no limitation on how many times you can use metamagic per turn. And the castings with these bracers are explicitly written to be two castings (first as an action, second as a bonus action), as quoted in your question.

So yes, you can twin the spellcastings as you describe, an action and a bonus action, in the same turn. You do have to spend sorcery points for both instances of Twinned Spell (2 sorcery points total, as both spells you’re twinning are cantrips).