Hi fatihaydin,
Welcome tom the Apple Community,
where some of us do our best to help each other troubleshoot.
Mmmm. Groups can be used in the Contacts app on Mac.
Email a group or Smart Group in Contacts on Mac
https://support.apple.com/en-au/guide/contacts/adrb475c5d8d/mac
Wondering if you might want to use iCloud with your iPhone.
It seems there is 5Gb free space for all Apple users.
(More space is available for purchase)
iCloud Support webpage, with info.
https://support.apple.com/icloud
Set up and use iCloud Contacts
https://support.apple.com/en-us/HT205754
Create a group of contacts on iCloud.com
https://support.apple.com/en-au/guide/icloud/mmfba73c71/icloud
Delete or change a group of contacts on iCloud.com
https://support.apple.com/en-au/guide/icloud/mmfba73312/icloud
Sorry I have no experience with using iPhone apps for grouping contacts.
If you'd rather not use iCloud:
Here's where to send feedback to Apple, if you want to see changes.
There's a webpage for sending feedback:
https://www.apple.com/feedback/
Hope there's something useful to you here :-)