Can I add my spouse to my Apple savings account

Unfortunately, not at this time. Apple Savings accounts are available to Apple Card account owners and co-owners only. Joint accounts are not available.

This was the case when Apple Card was released too in August 2019. It was not until May of 2021 that joint Apple Card accounts became available.

If the account doesn’t meet your current needs, find an account that does. It’s easy to add a beneficiary to the Apple Savings account with POD (Payable on Death) benefits.

Update your Savings account information in Apple Wallet - Apple Support

That's a very important feature for families. Spouses should be able to share savings accounts. It's much less valuable without that basic feature.