Currently, the Pull Request activity endpoint does not work with filtering, even though it returns a list of paginated objects.
https://developer.atlassian.com/bitbucket/api/2/reference/resource/repositories/%7Bworkspace%7D/%7Brepo_slug%7D/pullrequests/activity

For example, the following request will simply return the list of objects disregarding the updated_on field:

curl -X GET -u <user>:<pwd> https://api.bitbucket.org/2.0/repositories/<workspace>/<repoSlug>/pullrequests/activity?q=updated_on+%3C+2020-12-10T00%3A00%3A00-07%3A00&sort=updated_on

This feature request is to add filtering to this specific endpoint.