Should I use Next.js v13?

Should I migrate my app to Next.js v13, or should I keep using v12 until v13 is stable?

Version 13 is stable, same for any version numbers of Next.js on the stable channel (i.e., not canary).

As of v13.4.0 (4 May 2023), the app router is also stable.

Keep in mind though that as of 4 May 2023, Server Actions are still in alpha (so not stable).