Issue Summary

If the organization has multiple site, project admins can see the users [Project settings] > [People] > [Add people] > "Names or emails" list.
They can see the users who are not added to the site but added to the same organization.

Select the user from "Names or emails" list and [Add] does not trigger the user invitation.
So the added user is listed in [Project settings] > [People], but they are not added to the site and granted the product access. They can't access to the project until the product access is granted.

Even the User access settings > User invites is configured as invite anyone, invite is not triggered.

Steps to Reproduce

1. In the single org, there are 2 sites (Site A & B). User X is project admin for site A, and User Y is product user of site B
2. User X add the User Y to the project via [Project settings] > [People] > [Add people] > Selecting "Names or emails" list
3. User Y is not received the invitation, and checking the User Y product access in admin.atlassian.com, product access for Site A is not granted.

Expected Results

Adding the user who belongs to same org should trigger the user invitation based on user access settings.

Actual Results

Adding the user who belongs to same org does not trigger user invitation.

Workaround

Add product access via admin.atlassian.com > [Directory] > [Users], and then add to the project