Currently, if you have lots of files in a pull request, you'll have to navigate to the Files tab to view those files.
You can scroll using your mouse wheel or computer touchpad scroll.
However, there is no visible scroll bar for the Files tab.

Feature enhancement:
It would be very useful to have a vertical scroll bar visible on the Files tab for control and visibility over all files you can navigate

Latest update from Atlassian 2024-06-18

The updated Bitbucket Cloud pull request layout includes a visible vertical scroll bar for the file tree.