Since I’m not having any issues with Custom Theme Typography on my websites, I assume that your setup may not be configured correctly.
Could you show all the settings you’ve applied for Paragraph, H1, H2, and H3?
Also, please show whether you’ve configured the correct settings under Font Family — meaning whether you selected the correct font type and what your Font Family setup looks like.
Otherwise, without access to the project, it’s always difficult to say what exactly is causing the issue. If you want, you can send me the link to your project file via private message, and I’d be happy to take a look.
And now that I’ve just noticed it — it could also be because you set the wrong <base href="/blogg/" />.
Since your blog posts are actually located under /blogg/innlegg/, try using: