Where did my Gmail emails on phone inbox go?

hi all
sorry if trivial. i'm still learning iphone. set gmail via exchange can push feature. while noticed whatever in inbox (online gmail) same on phone inbox. see phone inbox doesn't have same ones inbox in gmail account. i'm confused why? don't recall ever deleting them phone inbox. besides, if did, have removed them gmail account well.

insight appreciated. iphone purge emails after many days?

 

arghhh...now noticed in gmail account see labels have "zero" emails in them. oh no did go????

 

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