emails deleted on iphone are not deleting on gmail server

Please see the pic below which is Self-explanatory for Gmail Account for other accounts please read below.

If you use an Exchange account, you can choose to store draft, sent, junk, and deleted messages on the server, and when to erase junk and deleted messages.

On other email accounts, choose Archive instead of deletion.

Settings > Mail > Accounts > [Tap and open the email]

Outlook / Exchange: Tap on Account > Advance Settings > Check what you need to delete Mailbox or Archive Mailbox

[Move Discarded Messages into]

Gmail / Yahoo / AOL: Tap on Account > Advanced > Check what you need to delete Mailbox or Archive Mailbox

[Move Discarded Messages into]

iCloud: [Scroll Down] Under Advanced Section: Mail > Advanced > Check what you need Deleted Mailbox or Archive Mailbox

[Move Discarded Messages into]

What you check here is what you get when you swipe left on an email message.

Check your WiFi Router / Modem for --> Recommended settings for Wi-Fi routers and access points ...

Connecting to Wifi is the first part and then getting connected to the Internet is the second

1. If you connect to Wifi, doesn't necessarily mean you are connected to the internet. If you are not connected to wifi could be a problem with iPhone settings or Router/Modem Settings
2. If you are not connected to the internet is the sole issue of Router / Modem Settings. Contact your ISP immediately

For your Internet connection.

• Over Cellular: contact your Carrier (Cellular Service Provider). The agency who issued the SIM to you
• Over WiFI: Contact your ISP (Internet Service Provider), the agency who provided the Internet Service on your Modem/Router to you

However --> Connect iPhone to the Internet - Apple Support

Are you archiving or deleting is not clear from your post?

Is this your corporate iPhone? Do you have any profile installed by your corporate / organisation / enterprise / School Management then please contact the system administrator of your corporate / organisation / enterprise / School Management

If you use an Exchange account, you can choose to store draft, sent, junk and deleted messages on the server, and when to erase junk and deleted messages.

On other email account choose Archive in stead of deletion.

Settings > Password and Accounts > [Tap and open the email]

Outlook / Exchange: Tap on Account > Advance Settings > Check what you need Deleted Mailbox or Archive Mailbox

[Move Discarded Messages into]

Gmail / Yahoo / AOL : Tap on Account > Advanced > Check what you need Deleted Mailbox or Archive Mailbox

[Move Discarded Messages into]

iCloud: [Scroll Down] Under Advanced Section: Mail > Advanced > Check what you need Deleted Mailbox or Archive Mailbox

[Move Discarded Messages into]

What you check here is what you get when you swipe left on an email message.

Are you using the Gmail app or the iOS mail app is not clear from your post.

Google Mail is not an Apple product. Contact the app developer here --> App Support or Gmail Help - Google Support