Terminology – What is a Person Who Works in Reinforcing Steel Called?

I suspect participant may be more common, particularly when pluralised, but that may simply be because it's a more common word applicable in many other contexts. For a single individual in this context, respondent seems more precise to me.

It's less common, but I think interviewee is equally suitable in OP's context.

I take it that you are asking for a technical term used in the formal linguistic study of grammar.

Within that domain, the questions you ask in the title and in the body of your question are really two different questions, and require two different actions. Permit me to rephrase a little.

What do you call the person who ‘does’ the verb [in a sentence]?
This is a syntactic entity and is called the subject of the verb or sentence.

What do you call the person who performs [the] action [expressed in the verb]?
This is a semantic entity and is called the Agent of the sentence or proposition.

It is important to distinguish these two entities, because in some sentences they may be different persons (or animals or institutions or in fact any noun or noun phrase – they need not be persons).

In the sentence “John killed Frank”, for instance, John is both the subject of the verb kill and the Agent of the action the verb expresses. (Frank, by the way, is the direct object of the verb and the Patient of the action it expresses.)

But if you recast the same sentence into the passive voice, “Frank was killed by John”, Frank (which was the direct object in the previous sentence) becomes the subject of the verb—but John is still the Agent of the action.