Can I legally record my California move-out walkthrough?

Yes. You're lawfully in the unit on your own move-out day, and recording video of a space you're legally occupying isn't something a landlord can object to after the fact.

The version that actually holds up in front of a judge isn't a quick pan around the room, it's a slow, narrated walk through every space, with your phone's date visible somewhere in frame at some point. Five unhurried minutes like that, taken the day you hand back the keys, tends to outweigh photos taken after the fact, since the timing itself is part of what makes it credible.