Do I care about phone security and updates?

Your phone can receive data from all sorts of potential input vectors. For example, someone can send you a text message that contains a document that your phone tries to preview that ultimately results in running code without your permission on your phone. Fake cellular base stations can attack the modem on your device. Bluetooth and Wi-Fi devices in physical proximity still produce radio packets that will be processed by your device even if you’re not actively joined to the same network.

These aren’t merely theoretical attacks either. They have been used in high profile cases to attack journalists and political figures even on devices that are up-to-date. Unless you’re using your phone exclusively in airplane mode without connecting to any networks or transferring data onto the phone of any kind, you are at increased risk.

EDIT: I wish to provide some practical advice. If you're not likely to be specially targeted by a threat actor and you don't process sensitive information on this phone, it's probably not terrible to use it anyway, although you do so understanding and accepting that there is increased risk in using a device that's no longer receiving security updates.

Occasionally you’ll hear about an unauthenticated race that only takes receiving a text.

All vulnerability services consider end of support to be a critical vulnerability.

My wife has the 4a. She's happy with it. I love how it fits in my hand.

But, I've been pushing her to upgrade because it's been out of security updates for over a year.

You may have a look at GrapheneOS or other custom firmwares for your Pixel 4A to get an extended period of security patches.

https://grapheneos.org/releases