Keep your original JPEG or editing project as the master and create a WebP copy for delivery. That lets you make different sizes later without repeatedly compressing an already compressed export. Use clear filenames that identify the subject and intended placement, rather than replacing every photograph in your archive with a new format.
WebP is an option for website photographs, but your content management system must accept the upload and serve the output correctly. Check that workflow with one file before converting an entire library. Some systems generate their own alternatives or resize uploaded images automatically. If yours does that, compare the file actually delivered to visitors, since a locally optimized file may be processed again after upload.