It's going to be incredibly difficult to disentangle exactly what went into this piece of decision-making.
You have basically have 3 different models to look at:
"Yes men", with the top leader having pliant underlings who meekly go along. Putin making decisions solo and imposing them onto others. The oft-reported episode of his spy chief getting told to "speak plainly" plays into that view. Note however that by its nature, a position like Putin's, or any singular leader (as opposed to explicit group leadership), slots neatly into that role: a leader is expected to lead.
"Eminence grise", or the "ones really pulling the strings" where there is the power behind the throne who "influence"/"convince"/"make the decisions". That's one possible way to take this question.
"Group think", where a small group of like-minded people exhaustively dissect the options, all the while ignoring the input of people holding different opinions. That's the other role for strongpeople ... with who have an interest in the war in this question.
Now, let's take the US's invasion of Iraq in 2003. All 3 are candidates, having been cited by different people at different times:
- Bush goes to war because Saddam went after daddy. Everyone else goes along.
- Cheney was the one who was the biggest, most forceful, hawk and imposed the decisions on the rest.
- The Bush team, while not intellectually lightweight, was incredibly cohesive in their worldview, from Condoleezza Rice to Rumsfeld to Cheney... The only one with a diverging outlook was Colin Powell and he got sidelined.
Twenty years after the war, it is still hard, with the degree of transparency found in POTUS archives and the publication of numerous books, to disentangle how the decision to invade was arrived at.
It's probably not Bush imposing on others, at least outside the bounds expected of POTUS leading, and it's probably more group think than Cheney pulling the strings, but...
Attempts to do this in real time in 2022 with Putin, from openly available sources are just going to reflect the biases and hypothesis of whoever writes up the analysis.
That said, we can look at some things we do know:
This playbook has been in play since 2008, when Russia backed separatists in Georgia, so whatever is influencing Putin is not new. So it can't be solely due to new guys. The Russians in country X are getting mistreated and therefore justify our interfering in that country is old, old, old. In fact, as old as Estonia in 2007.
A number of his close cronies are from his St. Petersburg days. These are people who were pulled up by him. They are more likely to be "yes men" or participants in a "group think" phenomenon than pulling the strings. One of them was Naryshkin, Mr. Public-Dress-Down.
The armed forces can't be too influential or else they would have told Putin not to invade with troops that had only been told to prep for an invasion the day before. That's basic military 101:
Mr Putin's initial military plan looked like something devised by a KGB officer, one Western intelligence official explains.
It had been created, they say, by a tight "conspiratorial cabal" with an emphasis on secrecy. But the result was chaos. Russian military commanders were not ready and some soldiers went over the border without knowing what they were doing.
So I would hazard to say that it's Putin's decision and mostly just his, reached in a context where only people liked by Putin are asked for their opinion. Sure, some of the people listed are going to be hawkish, but their presence is because they are agreeable to Putin, not because they are directing his decision making process. Putin also has a history promoting ex-body bodyguards and the like, hardly people who will direct him. And he seems to fancy himself a historian, which points to independent thinking to convince others, not the other way around.
For people to have had any direct influence on this particular decision, now, requires them to be part of the inner circle of decision makers who planned this. As opposed to merely people whose worldview agree with and have shaped Putin's own worldview. That's a limited circle, which does not necessarily include people who hold influential, but peripheral, positions.
But... if we don't really know all that much about Bush-Iraq 2003, how are we going to know Putin-Ukraine 2022, now?
Sources: DW and BBC. Guardian A 2017 version by CNN.