In 2022 it is no longer possible to see someone's activity on Instagram because Instagram (Meta ex. facebook) has removed the functionality to track a person's activity.
In 2022 you can still see some of someone's activity, including :
Their latest posts by going to their Instagram profile (if public profile, not private)
If the person is online by going to Instagram Messaging and looking at the date and time of their last connection (private message)
Their latest subscriptions by going to their latest subscriptions (see full guide above)