How much access does the email service provider have to my Delta Chat

Lets say I’ve set up a gmail account, and used this for creating a delta chat account.

Once I have established a chat with someone and the end to end encryption is running, then the messages sent through the gmail email servers are encrypted and no one at google can read them, correct?

So what access can gmail get? Are they able to login to my delta chat on another device as they will have access to my gmail account. Or is a delta chat account purely on one device, say my phone, and the end point of the e2e encryption is on the phone and there is no way for anyone at google to access it?

There is no such thing as a delta chat account: delta chat at the end of the day is an email client like thunderbird can be (although a bit peculiar), or if we are talking about gmail it could be a “replacement” for the google app. So you don’t create a gmail account and then a delta chat account, you simply access your gmail account through delta chat.

That’s right

As I said before there is no delta chat account, only a gmail account managed with the delta chat app. Delta chat uses pgp encryption via autocrypt, this means that the cryptographic keys are generated and stored on the device and the private key never leaves the local storage of the device so if the keys are not compromised no one other than the recipient and sender will be able to read the contents of the messages. What google will eventually be able to access is the metadata i.e. recipient, sender, time of sending and, I believe, size of any attachments.