Can I connect my Starling GBP and Euro accounts at the same time?

Indeed you can have different currency accounts under the same user, the same debit card.

When you navigate your profile, you may believe that they are the same account however, this is actually not the case. They are two different accounts with different identifications: The GBP account has a sort and an account number, and the EURO account has an IBAN and BIC.

Why can I connect both of the accounts at the same time?

Furthermore, given it's the one card, it will be one consent when connecting through TrueLayer. As Starling only allows one consent per Third Party Provider (TPP), see here for more info, when someone wants to connect a different account separately, they will be disconnected from the previous one.