"We incorrectly stated that PlayStation Plus is required for local co-op splitscreen play. Local splitscreen co-op requires a PlayStation account for each player but does not require a PlayStation Plus account." - Halo on Twitter
Good to see that you don't need PS+ for both players, that would have been crazy!
* XBOX Series X|S: If you’re playing splitscreen local co-op on an XBOX console, both players will need a unique Microsoft account. Online network co-op play requires an active XBOX Game Pass subscription. * PlayStation 5®: If you’re playing splitscreen local co-op on PlayStation 5®, both players will need to be signed into PlayStation accounts and be linked to Microsoft accounts. **A PlayStation Plus account is NOT required for local splitscreen co-op**. Online network co-op play requires an active PlayStation Plus subscription. * Steam: If you’re playing via Steam, you will need to link to a Microsoft account. #games