Is there a noun for people who have already completed their work and have free time? They are about to help others in other activities. I thought of idle people/idlers but that word seems to suggest the person it refers to deliberately avoids work.
Actually, I think good-old "free" is the best choice, as in:
having no obligations (as to work) or commitments;
not taken up with commitments or obligations;
not obstructed, restricted, or impeded;
not being used or occupied.
I'm not sure what you mean by "They are about to help others in other activities", but I presume you mean that, in a work situation, they have finished their task but are still at work (and expected to be working). In this case, you would not call this "free time", as they are not completely at their leisure. "free time" is usually reserved for non-restriction, such as outside of work, or during work when there is absolutely no work to do and no one to help.
Referring to the person as "free" is still appropriate, mostly in the sense of the last definition: they are "not being used or occupied". It is common to ask someone in the workplace "Are you free?" meaning are you not busy so that you can help/do something?
"idle" would suggest that the person is not doing anything useful. Assuming they are about to help others, they are not really idle, but they are free to help others.
"available" is also perfectly appropriate; "are you available?" is in fact a more formal way to ask "Are you free?"
I think idle fits. It has several meanings and two of them may fit in this context. What confuses you is the noun idler. But if you use the adjective idle with the word person, it may convey the message.
Idle (adj) - not in action or at work; not in active use
I work with an IT company and often use this phrase with my managers.
What about that php programmer? ~ Yeah, he's sitting free/idle. Yesterday only he completed his project - If you say the sentence in this way, it'd mean a person is sitting free and is not an idler.