My question is whether (and if so, how) you can modify settings so that some styles are available for every project every time Pro opens? I know in general, the new workflow is to add only the styles that are needed for an individual project, however there are some styles that we use for every project and would be nice to have them in there already. Any help would be appreciated.
You would create a template with the style(s) that you want to always be available, and then create projects from that template: https://pro.arcgis.com/en/pro-app/help/projects/create-your-own-project-template.htm
Longer term, there is some lively discussion about https://community.esri.com/ideas/14277-pro-importing-styles-should-be-permanent You could vote and add comments there.
Hope this helps you keep moving forward!