I feel if an app changes ownership, all users should automatically be notified by the app store.
Unfortunately defining what that means becomes rather tricky once you consider that the company owning the app can change ownership. That ownership can be shared and go through arbitrarily many indirections, and if it's a publicly traded company, some of its shares change ownership all the time.
There is no simple rule that can be applied at scale. Determining beneficial ownership requires a case-by-case review of not just the chain of legal ownership, but management, contracts, incentives, etc.
Any fixed rules can be gamed. For example, a company could license out its name as a "franchise" who is legally independent but whose franchise contract has so many arms of control that they de facto function as a single company. Another example is that a majority donor of a nonprofit controls the nonprofit even if they have no board seats or de jure power to appoint or fire board members.
For private, large companies, its a simply attestation. You could open source monitoring for changes - if the company makes an PR announcement of any kind , or if a member of the public reports submits proof of change of control exercise in their contract, ask the company to update their attestation and compare.
They don't provide it ? They get a nice little red banner alerting users of shadiness going on.
I realize this sounds tongue in cheek but a PE firm trying to get around ownership disclosure requirements can do something just as easily, both with public and private companies.
Indie app A, owned by a developer, Joe. Company B buys A outright, including employing Joe. They keep the brand around for name recognition.
How does the app store know this? None of this has to be public info if A & B aren't public. The company registration hasn't changed. At best, maybe the bank account number changed.