Vaccines not appearing under Immunization tab in Health app

The solution that worked for me (under iOS 15.1):

• Settings >> AppleID, iCloud, Media &Purchases >> iCloud >> turn on syncing Health data
• Wait a couple minutes
• Quit Health App
• Start Health App
• Bingo, immunization tab shows the vaccinations

This answer is useless. The OP did not ask about adding anything to the Wallet, but about the discrepancy between All Records and Immunization tabs.

I have the exact same misbehavior: I can find my immunizations in the All Record list (after lots of scrolling), and added my Covid record to the Wallet from there, but the Immunizations tab shows a completely blank screen. The health provider is Kaiser, which does support verifiable health records.

To be added to Wallet, the provider must support Health Records on iPhone and verifiable health records. You likely have a provider that does not support either.