This article explains how we can retrieve markdown content from a Bitbucket private repository managed by Google or others.
Instructions:
Go to Bitbucket and create an app password by navigating to your profile → Personal settings → App Password.
Log in to Confluence as an administrator and create a markdown profile by navigating to Settings → Markdown configuration → profiles and then click Add profile.
In Profile section, enter Profile name, choose Profile type as URL and give the URL of the markdown file like https://api.bitbucket.org/2.0/repositories/$workspace/$repo/src/$commit/$filepath
Provide your bitbucket user name and password that is produced in step# 1.
Use Markdown from a URL macro in your confluence page and provide created Profile name to show markdown content.