I've never heard that you must pray out loud. I guess it could be true for the Lord's Prayer, "when you pray, SAY..." But where in Phillipians 4:6-7 is the "out loud" part?
https://www.biblegateway.com/passage/?search=Matthew+6%3A6&version=NIV
Matthew 6:6
New International Version
6 But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you.
anyone who prays in public is a scumbag piece of shit liar
and as per philippians 4:6-7 you must speak your prayer out loud
so, that's two consistent points in favor of the idea you need to pray in private, out loud
if your social situation denies you this privacy, you need to change your situation
Discussion
yeah, neither matt 6:6 or philippians 4:6-7 explicitly say you must speak out loud but especially the matthew verse kinda implies this in the way it specifies requiring privacy
that also contradicts the common practice of preachers performance praying too, but not the speaking part
the speaking part is something i discovered myself, i'm sure there is more explicit indications of this somewhere in the bible though
i simply am in no doubt about it because of the experiences i had when i first started doing this, and getting answers both in action (people appearing to help me) and actually hearing words appear in my mind that were answers
anyway, YMMV probably but if you ever were thinking of doing something to switch up your prayer practice this is one i highly recomend