This may be obvious to a lot of folks but embedding iframes can be a confusing topic to many. John Mueller of Google confirmed that if you embed an iframe that contains a meta noindex, it won’t result in the page you are embedding the iframe being removed from the Google index.
John Mueller was asked this on Twitter and he said a simple “no” to the question, here it is:
— ? johnmu of switzerland (personal) ? (@JohnMu) July 22, 2022
This is not to be confused with the newish indexifembedded robots tag.
Of course, you can easily test this by using the URL Inspection tool in Google Search Console. That would very quickly verify if the page can be crawled and indexed and if not, what is preventing it.
Forum discussion at Twitter.