You can forget about embedding a movie in Pages and sharing it with others in different exported document formats other than Pages, or EPUB. Although the latter works in Apple Books, there is no guarantee other EPUB readers will support it. Adding any video of substantial length will result in huge file exports.
One can export a .mp4 video to Word, but this will create a folder bearing the name of the exported DOCX. Inside that folder is the Word document (foo.docx.docx) and the separate .mp4 video which is linked to the Word document. When one opens that internal Word document, one must first grant permission to access the movie before double-clicking it in the Word document and initiating playback. This is not a sharing-friendly approach.
One can export the Pages document containing the video to a Fixed format EPUB and open it in Apple Books. Double-clicking the video may be ignored for a while before normal playback begins.
Pages will not export a functional video to PDF. For that capability, you will need to use a paid PDF Editor to drop the video into the Pages exported (without video) PDF.