You mentioned "publishing pages", but you also mention using the power bi part. "Publishing pages" references a feature in "classic" mode, where we have a large degree of control over the html/css. Instructions for this are well documented, and have not changed in years. But, the fact that you're using the power bi part and are complaining about whitespace suggests that you're dealing with a sharepoint page in "modern" mode. Modern pages do not have any OOB customization options for modifying the HTML/CSS. The usual answer is that if you do not like a particular web part, then build your own using Visual Studio Code and SPFx (I know, not a feel-good answer for most).
You can find blog posts that explain how to create custom extensions that then allow you to inject css, but the standard warning applies: any changes you make via these mechanisms are outside of the recommended options, and if MS changes their master pages, your solution could break.