This is an intimidation tactic and not a real threat. If the vague threat is enough to prevent something from happening, then it has served its purpose. If not, then the vagueness gives an exit to do nothing.

Pretty much every country that has joined NATO since the end of the Cold War has seen a flood of such threats, Finland and Sweden most recently[1]:

  "Finland's accession to Nato will cause serious damage to bilateral Russian-Finnish relations and the maintaining of stability and security in the Northern European region. Russia will be forced to take retaliatory steps, both of a military-technical and other nature, in order to neutralise the threats to its national security that arise from this."

Russia has attacked only Georgia and Ukraine, the two countries that did not end up joining NATO. There, the threats achieved their goal and shaped the battlefield in favor of Russia, which was then exploited. Elsewhere, the fake act of "We're soooo concerned with our national security" did not yield the desired results, and Russians moved on.

Burns and many other Western diplomats have been surprisingly ignorant of such games, treat Russians as primitive savages who are incapable of manipulating people (despite it being a deeply ingrained feature of their culture), and take their words at face value, which produces the kind of memos Burns wrote. The 2008 decision to deny Georgia and Ukraine entry into NATO is nowadays widely considered a mistake. The views Burns held and promoted in the memo made the war more likely instead of preventing it.

[1] https://www.bbc.com/news/world-europe-61420185

> Burns warned of serious consequences arising from NATO’s eastward expansion to include Ukraine and Georgia

And then Ukraine accession disappeared from the policy menu. Then Putin annexed Crimea. Pretending Putin invaded Ukraine with any more strategic coherence than Trump going into Iran reveals a reality-defying bias in a source.

NATO doesn't expand eastward. Countries that see Russia as a temu-tier empire seek a defensive partnership.

The cold war is over, Russia lost in everyone's mind except the second rate KGB officer who now runs the country.