TYPO3 Core

Given you have a TypoScript with a cache configured:

lib.header = FLUIDTEMPLATE
lib.header {
    cache {
        key = site-header
        tags = pages
        lifetime = 15552000
    }

    file = EXT:example/Resources/Private/Templates/PageSections/Header.html

    dataProcessing {
        10 = TYPO3\CMS\Frontend\DataProcessing\MenuProcessor
        10 {
            levels = 2
            includeSpacer = 1
            as = mainnavigation
        }
    }
}

The first time this snippet is rendered, the cache tags are not added to the page. When the TypoScript is not rendered and fetched from Database, the Cache-Tags are not available and also not added to the page.
There was a change https://review.typo3.org/c/Packages/TYPO3.CMS/+/63768 a view years ago, which fixes that for the page cache, but this feature is currently not available for the hash cache.