Why would Putin benefit from having a Russian plant as the presidential candidate of the Green Party? Does he mistakenly think the Green Party has some influence in American politics?

They aren't intended to win, they're intended to do exactly what they're doing - selecting particular wedge issues to split the Democrat vote and give them a lower total percentage vs Republicans, the other main player. In this case the Green Party was originally set up to champion environmental issues, hence their name, but have also been a convenient shunt for the Israel/Palestine situation and Harris' percieved refusal to budge on such.

Everyone involved knows that a third party has no realistic chance of victory in the US, so setting up a third-party honeypot to gather passionate far-left voters away from the Democrat vote is a potent power move for the Republican party. Every percent point lost by the Democrats is one gained for the Republicans, even if the point doesn't go to them. With margins as thin as they usually are, this is significant. Putin in particular cares about this because Trump is vocally friendly towards him and Democrats and their voters are not.

And how could he known his plant would be selected by the party as their presidential candidate? Is he psychic? Is the entire Green Party comprised of Russian plants?

I can't find proof of this with a cursory web search, but it's suspected that the entire Green Party is primarily funded via Russian interests. If nothing else it is known factually that Jill Stein has attended at least one private dinner with Russian heads of state and has appeared on Russian state media propaganda quite a lot. I doubt the entire party is a Russian op but significant portions of its leadership including candidate Stein are pretty clearly compromised.

If his goal was for the Greens to be a spoiler for the Dems, surely they’d be just as much of a spoiler no matter who their candidate was. In fact, without Stein, they could probably find a better candidate and be more of a spoiler.

Personally I feel that Stein may just be more who they got rather than who they wanted, and this may be where the plan is starting to fall apart. A truly passionate, honest far-left firecracker candidate probably would be an excellent spoiler, and pull many honest far-left votes, but they also wouldn't be susceptible to foreign influence. They're choosing to take the bird in the hand, rather than two in the bush, and Stein is who they've got that they can control.

At the end of the day Putin has a very clear motive to help Trump win his election at all costs and the leadership of the Green Party has been shown to have been in close contact with Moscow. It may not matter materially whether or not she is a Russian plant at this time. But it does matter because it is yet another avenue for hostile foreign interference with our election.