Hey there bojengel,
Thanks for asking the Apple Support Communities about issues with Gmail between your iPhone and the webmail.
Check to see if your account is set up as POP or IMAP. You can search your email address here: Mail - Official Apple Support
If it is a POP email account, then this is working how it should. If it is supposed to be an IMAP account, next we need to check if a settings changed on your iPhone or Mac (if you have one).
If you're not able to complete these steps, or if you have any questions about these steps, please contact your email provider.
Use these steps to avoid removing a POP account and losing your data. You should also make a backup to ensure you have everything saved before making changes: Back up iPhone - Apple Support
- Open Settings > Passwords & Accounts > [click on POP Mail account] > Slide “Mail” to off. This will disable the POP account but keep the email messages.
- Go to Passwords & Accounts > Add Account. Then add the email account using IMAP. Use the IMAP account going forward for sending and receiving emails.
Keep the disabled POP account as an archive of email messages sent and received prior to disabling it. You should not to delete that POP account, as it contains your user data.
If the above steps do not work, and your Email Service Provider states it is an IMAP email account, please contact Apple Support to investigate this further with you. Get Support
Cheers!