How can I delete email account without loosing contacts?

Try to export the contacts from google mail on a web browser. During Export select export as vCard and then

log in to https://www.icloud.com using your Apple ID credentials Tap Contacts app > Settings > Import vCard.

Transfer the contacts from one email account to another.

Unlike some Android devices, contacts are neither stored locally on an iPhone nor in SIM. They are synced to an email account that you had Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

If Contacts on iCloud, try this --> Restore contacts, calendars, bookmarks, and more using ...

Else add the email account that stores your contacts.