Don't Want to Redo All Formatting

For my most recent project, I have everything set up for formatting: Section layouts, section formatting etc. For example, under My Formats I have a format called “My Bookfunnel PDF.”

I opened an old project and had Scriv convert it to the new version. I went to compile it, but found that even when I chose “My Bookfunnel PDF,” I had to to assign the formats and do the formatting.

How can I avoid that?

If I’m understanding you––it sounds that you tried to compile a converted project before setting the correct Section Types for the project. For stock Scrivener templates like the Novel one:

The above is from the document titled Setting Up Section Types included in the downloadable project at Scrivener 3: A Guide for Scrivener 2 Users: … date-guide

If it’s not a stock template (regardless, it’d be worthwhile to check), before compiling you’d need to set them manually at:
Project > Project Settings > Section Types