Not sure that Google offer Takeout on Business Profiles. Businesses aren't often protected by the kinds of PII-protecting laws (GDPR etc.) that individuals are, and so tech companies are less-inclined to make tools to streamline bulk export of data.
So was the identity verification process you spoke about in the blog post for your personal account or your business profile?
If it was your personal account, I really don't see how a personal verification ends up on a business account. I'm not saying it's not possible, but it seems like it would introduce extremely bad data. I've verified my phone number, but (personal speculation) I doubt Google would want my number showing up on my employer's business profile.
If it was for your business account... I can see how that would be unexpected, but also the point of verifying that would I guess be to increase the level of trust that customers could have in the business based on it being verified, and I can see how that might lead to that number being public. It also sounds like this is what you did with Play too, and as a user I would expect that Play's company data aligns with data on Google Search.
I can empathise with the shock here, I've had people call me up from google searches and finding my number on my CV, but I am struggling to find a link here that doesn't make sense.
I wanted to take control of the Google Business Profile (back then: Google My Business) listing. To do that, Google asked for a phone number they could call. I provided one, and then double-checked that they hadn't put it on the public profile (they hadn't).
They emailed me about once a year after that to suggest that I might like to put a phone number on the business profile. I declined. But I always checked, and sure enough: they hadn't put one on there. All was good.
Then one day, randomly, my phone number started appearing on the public profile/being served to search users. That's the whole story here.
I don't yet know how or why it started appearing. A few ideas have been posed here and elsewhere, including:
1. Some runaway automated process at Google, trying to "fix" the absence of a business phone number, took the one that was previously used to ID the business contact. (Some folks seem to think that this is what I'm claiming happened, but I'm only putting it forward as a possibility.)
2. Google "joined the dots" from the Google Play profile and the Google Business Profile. This currently seems like the most-likely explanation, to me. I'm getting the former corrected anyway; we'll see what comes out of it.
3. Some third-party Google user added it. That seems possible, but in my experience once you've verified and own a Google Business Profile, you get an email to confirm any "suggested changes" and I didn't see any such email.
4. Some kind of user error by me or by somebody else who has access to the profile. I obviously can't rule this out, but I've checked and I personally haven't even logged into it in over a year (and I've had emails since that confirm that a phone number wasn't listed), so it seems unlikely. Also, the message said that Google had updated the phone number (not me).
This list seems reasonable, but I do think your blog post strongly implies (to the point of effectively stating it) that you believe (1) was what happened.
I have to be careful about what I say, and very much cannot say in this case, nor do I know anything specific to the business profile area, but my experience of data at Google is that one does not simply join a table and fill in the blanks. In my experience there's a lot of privacy and legal review, and that's only after someone thinks it would be a good product idea (which in this case feels unlikely). At a technical level, there are many safety checks that are intended to prevent things like this from happening unless all that review and sign-off has happened.
If I search my phone number on certain online white-page sites, every single house I've ever lived in for the last 25 years shows up in a list, along with a whole bunch of other very personal information (e.g. the people who lived in the same house at the same time).
Applying Occam's Razor here, the explanation given in the post seems like possibly the least likely option.
One way to shed some light on this would be to use Takeout to get a copy of data held and see if they still have the number and what they hold it for.