Oh, I'm sure many of the Russian people may have believed that, because they've been fed it as a useful line of propaganda by their own government. Gullible westerners have accepted and repeated that as well. But apart from being irrational, it is clear from the actions of the government that the Russian leadership itself did not share that fear:
First, Ukraine was nowhere near being admitted to NATO -- wasn't even on a timeline of any kind. And if it ever got to the point when there was the typical years-long timeline set, Russia knows that it takes a long time for that to happen, with lots of debates, benchmarks, etc., and that any one single member state could stop it. So the alleged "fear" of Ukrainian ascension to NATO was wildly premature.
Second, if Russia truly was (even if irrationally) afraid of invasion from the West, then why risk provoking the feared NATO into a military confrontation by invading Ukraine?? Russia's invasion of Ukraine actually strengthened NATO. Keeping Sweden and Finland out of NATO has been a major strategic goal of Russia for many decades, but this war caused that exact thing to happen. It further triggered significant rearmament by member states in the exact alliance Russia supposedly feared. That is not the action of a nation afraid of western invasion.
And Third, Russia was perhaps a three years away from having most major NATO powers completely dependent upon Russian fossil fuels. That alone would have been the perfect guarantee that Russia wouldn't be invaded, and Russian leadership knew that. But they choose to give up that additional guarantee of no western invasion to invade Ukraine. Again, emphatically not the action of a country motivated by fear of conflict with the West.
Anyway, that wasn’t why they invaded Ukraine, although the invasion may have happened later anyway.
Well, if you agree that isn't why they invaded Ukraine, then why do Trump and so many others make that patently false claim? Ignorance, or dishonesty? Because those are the only two options.
“Oh, I’m sure many of the Russian people may have believed that, because they’ve been fed it as a useful line of propaganda by their own government.”
If you consider Russian HISTORY to be ‘propaganda’, then so be it. But since our version of Russian History and the European version of Russian History PERFECTLY MATCH IT, regarding how Russia has been invaded, then, I guess they must be all lying.