At the end what worked for me is, I opened all groups (Gmail, iCloud, and other that I had) on my macbook. Then, I opened Contacts app on Mac. Then, I go to the group Gmail, click on one of the contacts and then just select all (CMD+A). Then I drag and drop all of these from the Gmail to iCloud (in the left sidebar there are all these groups listed, iCLoud, ...
This short AppleScript deletes all Outlook fields from all contacts. Optionally, it can also delete all notes.
tell application "Contacts"
delete (every url of every person whose value contains "outlook")
-- set note of every person to missing value
You have two options here - you can either keep the contacts in Google Contacts and add your Google account to the other phone so they sync, or you can transfer the contacts to iCloud. If you're only using Apple devices, my recommendation would be to transfer them to iCloud, because it's simpler to manage and works well with Apple devices. If you own Windows ...