How does the native mail app work with Gmail? Why did deleted emails show and then disappear?

So,

I am connected to my Gmail through the native IOS mail app. About 3 weeks ago I deleted a TON of old emails. That included sent emails. Keep in mind that I deleted these on the Gmail web page through my regular computer, not through my iPhone. I thought they would delete everywhere, but I guess not.

So today, I went into my sent folder and searched for the oldest emails possible, and sure enough, the emails I had deleted a couple of weeks ago on the Gmail web page were showing up in the native IOS Mail app.

However, they started to disappear after a few seconds and eventually they were all gone(as if they had been deleted).

I guess my question is why did the mail app still have my emails? Were these cached on the Apple servers, and once I searched them Gmail IMAP updated the emails as “deleted” so Apple iOS Mail app deleted them?

also to clarify, these were NOT archived anywhere. Not in Gmail and not in iCloud or the iOS Mail app. These were “permanently deleted” 3 weeks ago, and certain of it.