When I delete a message in Gmail is it really deleted? Or is it kept by Google for further analysis?

It is marked as deleted and its encryption keys are destroyed, at which point it immediately stops being used for anything.

But the email itself sticks around, encrypted, for a short while until the storage system does a garbage collection. That’s fine though, because the keys are gone and nothing can decrypt it.

Any analysis that would ever be done on an email happens while it is delivered, not after the fact.

As a G Suite administrator, you can restore emails that were permanently deleted by your users within the past 25 days.

For me, this implies that permanently deleted emails are just flagged until the storage system reclaims those precious bytes, not less than 25 days later.

While this applies only to G Suite administrators, I don’t see why the consumer Gmail product would work different, except that the Administrator is someone at Google.

More info here: Restore a user’s Gmail and Drive data

Now, on your question, I understand that you believe Google will analyze deleted emails because the action of deleting implies that there’s something important you want to hide.

While that would be a nice flag, if your email triggered any alarm, they would have analyzed and made a copy of the contents as soon as it arrived. No help deleting it.

More info here: N.S.A. Halts Collection of Americans’ Emails About Foreign Targets

/softly chuckles...

I can no more positively answer this question than anyone else - at least anyone who does not work at Google. And from the tone of the question it seems likely you would not believe Sundar Pichai if he answered you personally.

But I can suggest a little practical logic.  Google already has more such data for potential "analysis" than anyone else on the planet. If they are indeed analyzing your email, they already did that - when it was first sent.

Why would they want to keep what you delete?