A public company is privately owned. The "Public" refers ot the ABILITY of the public to buy the shares if they so choose. In this case the public consists of private individuals.
The term "Public company" refers to the fact that when a privately HELD company (i.e. not listed on a stock exchange) gets listed on a stock exchange, it is called a 'Public Offering'. It means that the shares are available to the public to buy, just like they can buy any other product or investment. But they are private owners, meaning not government.
If you buy shares in a public company, you are a private citizen. At that point YOU are involved in the company. The rest of the public is not involved, so it most assuredly is not everyone's business, any more than how the drycleaner decides to invest in a new dry cleaning machine is also not my or anyone else's business who are not owners of that same. business.
Public companies are required to disclose information and comply with securities regulations, as well of course with all sorts of other laws.
While there can be a confusion about public corps vs public comp. both are everyone business as they are as you say, in the public sphere. If one has a private company that robs is shareholders that only effects the shareholders. A public one, well , the enforcement or lack therefore effects all trades and the rule of law. It is everyone business in the way drunk driving is everyone business vs getting drunk and throwing up at home (which is private).
There are some cases of there a private company deals with the public that it becomes everyones business - private company doing goverment kidnapping contracts for example (Black Cube comes to mind)