Karlach, Fury of Avernus: Rules Question

My friend & I had a disagreement about how Karlach works.
Here’s a reference of her text:
“Whenever you attack, if it's the first combat phase of the turn, untap all attacking creatures. They gain first strike until end of turn. After this phase, there's an additional combat phase.
Choose a Background”
My friend says that First Strike only applies to the second combat phase, and only to the creatures that attacked in the first combat phase.
I think that First Strike applies to both combat phases, but only gives first strike to creatures that attacked the first combat phase.

Could someone please clarify?

Referencing rules would be appreciated!