12v battery test

Gen 3 2010.
So been having these ice start delays where the transition between battery and ice kicking in is sort of a push start feeling.

Switch car off press power button twice without brake pedal hold info tel button and switch lights on off brings you to service menu. Press function check/setting then vehicle signal.

Can someone tell what they get for battery.

Instantly after driving around im getting 11.7v 11.8v. Dropping all the way down to 10.4v when i out a load on it but then comes back up to 11.8v when i switch load off.
So I thought ok great ive got a bad 12v battery which is easy to do.

BUT at the battery with a voltmeter im getting 13.8v after shut down slowly going down to 12.7v max 12.55v after 30 minutes so that would suggest battery is good.

So if people with no problems can report theyre volts it would help.