Dear Umar Butt,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, please let us cooperate and please don’t worry, we can work together to narrow down and resolve the situation.
As per your custom created permission setting, I can confirm your permission is correct. When we click on "Add items" we can add documents to document libraries.
And only in case User cannot upload files if “Add item” is unchecked in a permission setting.
Generally, to only add files to SharePoint online library we open the Editpermission level and click Copy Permission Level on the bottom and then uncheck the Edit Items and Delete Items options.
Secondly, may I know how you grant the site permission to the user? please provide your detailed steps.
Site permissions>Grant Permissions>Invite people and type the user's email address> SHOW OPTIONS>select the new permission e.g. I named Upload>click Share
If possible and if you don't mind could you please you please try to create a new permission level named Uploaders and check the permissions Open, Add Items, View Items and View Pages. Then grant the permission level to the users and groups who should be able to upload documents but not edit and delete them and verify the result with us, it will help for us to narrow down your problem.
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Waqas Muhammad