Should the United States Fight World War III for Ukraine?

Let’s start with two stories.
The first is well known: After Adolf Hitler gained power in 1933, he rearmed Germany, withdrew from the League of Nations, remilitarized the Rhineland (1936), fought a proxy war in Spain, annexed Austria (1938), annexed half of Czechoslovakia (1938), and invaded Poland (1939). At every step, European leaders assumed they could stop further aggression by placating him with concessions, most famously with the Munich Agreement. They were wrong. The lesson every leader has taken for the past 80 years is that appeasement never works and leaders must show strength to face down bullies.
The second story teaches the opposite lesson and is not as well-known. In 1898, the French government sent troops into the interior of Africa to the Upper Nile river basin. The theory: If the French controlled the Nile, they could choke out the British, monopolize North African trade, even control the Suez Canal and shut down Britain’s access to India. As goes the Nile, so goes the world, was the theory. British and French troops met and faced off at a remote African town of Fashoda for nearly two months. London and Paris prepared for war, believing the fate of global empire hung in the balance. Cooler heads realized how ridiculous it was to fight global war for a remote bit of African desert, and war was averted. The less-well-known lesson: Not every crisis is the Archimedean Point upon which world order revolves.
As Russian President Vladimir Putin masses troops on the Ukrainian border, American observers are asking a series of questions. Is this Munich, or is it Fashoda? Is this a moment to project strength and face down an international bully hellbent on territorial conquest? Or is this a peripheral dispute blown out of proportion to which the responsible answer is not a war cry, but a shrug? Should the United States throw down, draw a line in the steppe, and relive its glory days leading the free world against tyranny? Or are we at risk of getting dragged into yet another unnecessary quagmire?