defining the subject

Indeed the entire clause 'All but Jones' is the subject.

I think this contains a good explanation as to why.

(What he had already forgotten about computer repair could fill whole volumes.

—the simple subject is not "computer repair," nor is it "what he had forgotten," nor is it "he." Ask what it is that "could fill whole volumes."

Your answer should be that the entire underlined clause is the simple subject.)

Who is here? All but Jones.

It is commonly asserted that the subject of a sentence is the noun or pronoun that does something or exists in a particular state of being.

First, this is not true. Oh, it's commonly asserted, certainly; but that's not what Subject means.

Therefore, in the sentence All but Jones are here ...

Sorry, there's simply no therefore about it.
You're working from a false premise, so you can prove any proposition you please.
Subject is a grammatical term, with a grammatical definition.
That means its definition cannot refer to what it means -- that's not grammar.
It has to refer to how it's used grammatically, which -- in English -- means syntactically.

There are a number of syntactic tests for Subject.
One of them is governing verb agreement, as you suggest.
Another is inverting with an auxiliary verb in questions:

• The prisoner is still being held.
  ==>
  Is the prisoner still being held?
• What he told you yesterday is still being denied.
  ==>
  Is what he told you yesterday still being denied?

Still another is B-Raising with Passive; this identifies the subject of an infinitive clause

• They believe [the prisoner to be guilty]. ==>
  The prisoner is believed to be guilty.
• They believe [there to be gasoline stored here].
  ==>
  There is believed to be gasoline stored here

As can be seen, subjects can be much more than one word; as for meaning,
quite often the subject has no meaning, like Dummy There in the examples above, or
Dummy It in It's raining or It's a long way to Tipperary.

Sometimes the subject can be even expressed by a verb:

To not approve means to disapprove

That is why it can be quite confusing to argue that a verb is a regular element of syntax structure, not predicate like in this Cambridge Dictionary article.