I see "Edit" button next to the comment where Im not an author.
@Eugenia Rubleva , Welcome to the Atlassian Community!
This happens because your user has the Edit all coments permission. You can read more about all project permissions and see what the impacts of each one: Permissions for company-managed projects | Atlassian Support
To configure project permission scheme is necessary to have the jira admin profile, but if you permission scheme is based on project roles may with the project role administrator you're be able to change something.
Hope this helps you.
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