why Typo3 website v10 show empty sitemap xml in frontend – SEO

If this is all you have, then you are missing some key configuration. You need to specify what should be shown. So, on your TypoScript, based on the documentation, you should define what pages/extension etc must be shown. For example:

plugin.tx_seo {
  config {
    xmlSitemap {
      sitemaps {
        pages {
          config {
            excludedDoktypes = 137, 138
            additionalWhere = AND (no_index = 0 OR no_follow = 0)
            #rootPage = <optionally specify a different root page. (default: rootPageId from site configuration)>
          }
        }
      }
    }
  }
}

Here is an example for the extension news as well, in case you are using it.

plugin.tx_seo.config {
    xmlSitemap {
        sitemaps {
            news {
                provider = TYPO3CMSSeoXmlSitemapRecordsXmlSitemapDataProvider
                config {
                    table = tx_news_domain_model_news
                    additionalWhere =
                    sortField = sorting
                    lastModifiedField = tstamp
                    changeFreqField = sitemap_changefreq
                    priorityField = sitemap_priority
                    pid = 26
                    recursive = 2
                    url {
                        pageId = 25
                        fieldToParameterMap {
                            uid = tx_news_pi1[news]
                        }

                        additionalGetParameters {
                            tx_news_pi1.controller = News
                            tx_news_pi1.action = detail
                        }
                    }
                }
            }
        }
    }
}

Here the documentation as well: Documentation