The Budapest memorandum was where Russia guaranteed in writing to respect the borders of Ukraine.
Tell me, what document or agreement was it again where who exactly promised not to expand NATO?
There isn't one and the alleged verbal promise probably did not happen:
“I was in those meetings, and Gorbachev has [also] said there was no promise not to enlarge NATO,” Zoellick recalls. Soviet Foreign Minister, Eduard Shevardnadze, later president of Georgia, concurred, he says. Nor does the treaty on Germany’s unification include a limit on NATO enlargement. Those facts have undermined one of Russian President Vladimir Putin’s justifications for invading Ukraine — that the United States had agreed that former Warsaw Pact nations would never become part of the North Atlantic security alliance."
Now, if there was a verbal promise made in 1990 it was only that NATO would not expand to the former GDR (which ship of course had long sailed by the time Putin went into Ukraine).
Further Yeltsin explicitly approved of the expansion of NATO into Poland, long after any such verbal promise may have been made. That resulted in the now near dead NATO-Russia Founding Act which also does not prohibit NATO expansion.
The Russian talk of the "broken promise" is as much of a pretext for the invasion of Ukraine as many other spurious Putin claims.