How do I verify my student status if I don’t have a ID card?

But it’s already verified through UNiDAYS

According to the Related Article -> Get an Apple Music student subscription -> it is sufficient if you already verified through UNiDAYS.

see point 5 ⤵️

How to get a student subscription to Apple Music

1. Open the Apple Music app or iTunes. 
2. Go to Listen Now or For You.
3. Tap or click the trial offer (one trial per person or family).
4. Choose Student, then tap or click Verify Eligibility.
5. You'll be taken to the UNiDAYS website where you'll need to follow the onscreen prompts to verify your enrollment. After UNiDAYS verifies that you're a student, you'll be redirected back to the Apple Music app or iTunes.
6. Sign in with the Apple ID and password that you use to make purchases. If you don’t have an Apple ID, choose Create New Apple ID, then follow the steps. If you're not sure if you have an Apple ID, we can help you find out.
7. Confirm your billing information and add a valid payment method.
8. Tap or click Join.

👉 then you continue with point 6 and on.

When I signed up for Apple Music last time it never asked me for my ID card just to sign up and verify my student email through UNiDAYS.

Not sure if you can ask twice for Apple Music (?)

Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)