Google has a bug in Google Search Console where it reported some sites being indexed using mobile indexing as being indexed using desktop indexing. I am sure we all have sites that are "mobile friendly" and also show that Google is indexing it using the desktop crawler, when they should be using the mobile crawler and this is why.
This came after Google did its last batch of moving sites from desktop indexing to mobile indexing the other week.
John Mueller of Google said on Twitter, "It looks like we're also showing the wrong mobile indexing status for some sites in Search Console, which is a reporting issue on our side (and also not related to mobile friendliness)."
Here is that tweet:
It looks like we're also showing the wrong mobile indexing status for some sites in Search Console, which is a reporting issue on our side (and also not related to mobile friendliness). I'm happy to check, but my assumption is your site is already in mobile first indexing.
— John Mueller (official) · #StaplerLife (@JohnMu) May 30, 2023
You can access to see if Google is crawling using desktop or mobile indexing in Google Search Console under settings, here is a screenshot:
Here is an example of a mobile-friendly site showing it is being indexed by the desktop crawler:
If you believe you should be on mobile indexing, then check back later after Google fixes the reporting issue.
We will likely update you when this is resolved, so make sure to stay tuned and subscribe.
Forum discussion at Twitter.