Utilities and infrastructure can be considered public goods insofar as they have the characteristics of non-rivalry and non-excludability, meaning that one person's use of them does not diminish another person's ability to use them and it is difficult to prevent others from using them even if they have not contributed to their provision.
However, utilities are typically excludable (service can be cut off for non-payment) and rivalrous to some extent (there are capacity limits and usage can impact others), so they are better classified as private or quasi-public goods.
So why is this idea so prevalent: that public goods should be public utilities?
A key driver behind the transformation of some public goods into regulated public utilities seems to be the theory of "natural monopoly," which posits that certain industries are most efficiently served by a single provider, making competition impractical or wasteful. Then in 1919 the economic theory of public goods, notably developed by Erik Lindahl, further contributed to the myth by arguing that public goods should be funded through taxation based on individual benefit. This reinforced the notion that the government should organize and finance such goods, often through public utility models.
So I wouldn't say public goods have nothing to do with public utilities.
As it relates to Google search, I think it is very difficult to construct an argument that search is a natural monopoly. There's no limitations on parallel processes the way there are with roads or railroads or electric infrastructure. In fact, people have access to a long list of competitors at all times.
You can make it much better case that they are engaging in monopolistic practices, which is a claim very different from a natural constraint
This doesn't follow from the linked article. Taxes can be levied in various ways, oftentimes related to usage. Involving a private entity doesn't suddenly change the nature of the thing. There's a marked difference between a sack of flour and my electric meter.
We as a society decide to make certain things into public goods. This is frequently the choice for natural monopolies.
Critiquing the article you linked - when taken literally non-rivalrous applies to approximately nothing. Non-excludability is simply a matter of law, which is a matter of what the voting public wants.
