I've set an "Default Assigned To" person in the activity. The admin user created the custom activity, the default assigned user is "User 1". Although User 1 can see the activity and edit it. as soon as the activity gets marked done, only the admin sees the activity log. User 1 marks the acitivty as done, the activity is no longer visible for user 1 but it's visible for the admin. so where can i set/change this behaviour?

You can use this app (search app in odoo apps by name provided below) to preview your own activities.

Apps Name:

Advanced Activity Dashboard