Not as far as I'm aware. You can query much of that stuff using the CLI with the .dbinfo command, but support for that appears to be dependent on build options so may not be available. Another option might be to provide multiple commands("sqlite my.db 'PRAGMA user_version' .dump"), but you'd have to remember to update scripts if you suddenly started using other things in your app too.
I'll note that the metadata is handled correctly by the CLI's .backup command or you can "VACUUM INTO <somewhere>"¹, so if you're just attempting to use .dump for the sake of backup there are probably better options available anyway.
But yeah, I was surprised when I chased down a bug that was caused by a missing application_id following a restore from .dump output. I did a search at the time and noticed it had been reported to the sqlite folks on their forums a few times, so presumably I'm missing the reasoning behind not including it.
¹ https://www.sqlite.org/lang_vacuum.html