@kingrat I do that, too. I also get their full list of vaccinations, not just Covid, and keep that in a file on my Mac and my iPhone. But I like having the physical card, too.
Sometimes the California record is wrong, and you have to write to them to get it fixed. They're good about making the fixes, though. They had my September 2024 Covid vax listed as a Tdap vax!
But the card that goes into an iPhone's wallet only has the last four vaccinations. (You can keep older versions to go all the way back, but I didn't realize this at first, so I'm missing my first two.)