It appears that Google Business Profiles is pushing more and more to verify their businesses using video verification. We covered this before, as Google set this as the default option, but not as offering video as the only option.
Jason Brown said on Twitter for the last number of verification attempts, he was only given video as an option. No other options were given to him he said and he wrote "Looks like Google is forcing video verification as there is no option to verify via postcard."
He shared this screenshot:
So I tried it immediately after I saw this tweet and the first verification worked automatically since I have the site under my email account in Google Analytics (and Search Console). For the second one, I took a random business and it only offered me a postcard option, nothing else:
Joy Hawkins added on Twitter "Yeah I can see them doing more and more of this."
So if you are seeing video only, you are not alone. Although, I see the postcard method and auto verification as options when I try it myself.
Forum discussion at Twitter.