You can always mention a user, but if you don't have Browse users and groups permission then user picker will only list assignee and reporter of the current issue (if they are set). Without that permission no other users will be suggested even if they would match your query.
Adding a mention
To mention a user type "@" followed by part of the user's display name (full name) or nickname (username). A popup will show up listing all users matching the query. You can change the selected user by using arrow keys and mouse. To confirm your choice and make use of auto-completion press Enter or click on a user in the popup:
Example of user mentions:
If your query is empty, i.e. the mention consist of "@" character only, the popup will show users related to the current issue: assignee and reporter (if they are set on the issue). You can also use two special aliases, "assignee" and "reporter", to find and mention corresponding users:
Internally mention stores "Atlassian account ID" of a user (due to GDPR). "Atlassian account ID" is a non-PII cryptic text like 557408:b0926d6a-bbb4-461e-a3e5-37858a82211d
Mention by email
Mentioning users by their email addresses is supported by Issue Checklist. The search will match partial emails for users who have made their email address public in their profile. Otherwise a full email address must be provided to match the user that needs to be mentioned.
Mentioning by email can yield weird results sometimes. Searching for user by providing incomplete email addresses may show no user at all in some cases because of an issue in the Jira software itself. We have observe that the following combinations did not yield appropriate results: