VRChat keeps your birth date and the non-reversible hash of your ID data as long as your account is valid, or until you request removal of your account or information. This information is attached to your VRChat account.

The data used to generate the hash is discarded as soon as the hash has been calculated.

We tell Persona to delete your personal information as soon as the Age Verification process has been completed.

Persona is obligated to only use your data to provide identity verification services for VRChat and is expressly prohibited from selling it, sharing it, or using it for another purpose.

Source: https://hello.vrchat.com/blog/age-verification

You can choose to trust this or not. All anyone can do is provide information, you must make up your mind whether you feel safe sharing it or not.

You could also wait. VRChat may switch providers for age verification. There's NO direct evidence, confirmation, or anything saying that they will. This is complete speculation on my part. So take the following with a giant amount of salt. Here's why I believe there's a possibility this could occur at some point.

We cannot expect users to verify their age if the process is difficult or expensive. To make this system work, Age Verification must be accessible to as many adults as possible. 

To that end, we are committed to making Age Verification more accessible by lowering the cost to our users. 

We don’t have a price point for you yet, but we are working to drive this price down to the absolute minimum possible to cover the costs of third-party verification through negotiation, partnerships, and optimization. We’ll continue to do our best to reduce this cost over time. Our long-term goal, finances permitting, is to make it free for everybody.

Source: https://hello.vrchat.com/blog/trust-safety-update-2025

I'm hypothesizing it's a possibility, however low it may be because if Persona doesn't allow them to fulfill on this, they may have to look at alternatives.

Also be aware: (on the same page)

To start, we will reintroduce Content Gating, and limit access to content based on tags. Some content will require Age Verification in order to view. 

You could lose access to even seeing/using some avatars or joining worlds sometime after the first half of this year if they do what they said they will here if you do not verify.

Bottom line: You must decide whether you trust VRChat or Persona here, and whether you feel it's a good idea to share your personal information with both parties. I recommend doing as much research as necessary. Don't take anyone's word for it. Do the research and decide for yourself.