I think you are giving far too much credit to Trump who will greedily claim it anyway regardless of whoever is actually responsible for it. Trump doesn’t do strategy. He reacts.
It seems to me that the real credit for putting the squeeze on Putin goes to the Ukranians. This is what Zelensky realesed earlier:-
“I received a report from our delegation on their meeting with the American team in Saudi Arabia. The discussion lasted most of the day and was good and constructive—our teams were able to discuss many important details.Our position remains absolutely clear: Ukraine has been seeking peace from the very first second of this war, and we want to do everything to achieve it as soon as possible and in a reliable way—so that war does not return.At this meeting with the Americans, Ukraine proposed three key points:silence in the skies—stopping missile strikes, bombs, and long-range drone attacks; silence at sea; real confidence-building measures in this whole situation, in which diplomacy is ongoing, which primarily means the release of prisoners of war and detainees—both military and civilian—and the return of Ukrainian children who were forcibly transferred to Russia.The American side understands our arguments and considers our proposals. I am grateful to President Trump for the constructive conversation between our teams.During today’s talks, the U.S. side proposed taking an even bigger first step—a 30-day full interim ceasefire, not only stopping missile, drone, and bomb attacks, not only in the Black Sea, but also along the entire front line.Ukraine is ready to accept this proposal—we see it as a positive step and are ready to take it. Now, it is up to the United States to convince Russia to do the same. If Russia agrees, the ceasefire will take effect immediately.”
So no backing down from them for the need to ensure “war does not return”, ie security guarantees. If Putin refuses Trump loses face. If Trump loses face because of Putin he could pivot again. No strategy. Just reactions.
I can imagine Zelenskyy offering to recommend Trump gets the Peace Prize in return for bankable security guarantees. Trump likes the attention and admiration. Peace Prizes. State visits. Trinkets as bribes to save lives.