How to avoid page breaks right after or in the middle of section titles in a EPUB book created with Bookdown?

Thanks for this MRE. Moving to an answer because that's easier to share code. I will delete if I'm wrong. It seems like, you have to use the stylesheet argument in bookdown::epubbook + the !important notation to enforce your styles.

# EPUB:
bookdown::renderbook(input="index.Rmd",
    bookdown::epubbook(figwidth = 5, figheight = 4,
        dev = "png", figcaption = TRUE,
        numbersections = TRUE,
        toc = FALSE, tocdepth = 2,
        stylesheet = "style.css",
        metadata = NULL,
        chapterlevel = 1,
        mdextensions = NULL,
        pandocargs = NULL,
        template = "default"
        )
    )
PDF:
bookdown::renderbook(input="index.Rmd", "bookdown::pdf_book")

styles.css

p.caption {
  color: #777;
  margin-top: 10px;
}
p code {
  white-space: inherit;
}
pre {
  word-break: normal;
  word-wrap: normal;
}
pre code {
  white-space: inherit;
}
.caption { text-align: left; }
/ my styles Id:1923170
I added !imporant here to overwrite any styles added by readers such as https://epub-reader.online/
 /
h1, h2, h3, h4, p { 
   page-break-after: avoid !important;  
   break-after: avoid !important;  
   page-break-inside: avoid !important; 
   widows: 3; orphans: 3;
}

Then my styles are applied; verified using this epub reader + using ReadEra on mobile.