COVID-19 Outbreak Information Updates (Reboot) [over 150.000,000 US cases (est.), 6,422,520 US hospitilizations, 1,148,691 US deaths.]

Since Omicron, completely true.

Not true at all with Alpha and to a lesser extent Delta.

There was about a 2-3 month period in November-January where it became really clear that the vaccine was not having any significant impact on infection where people were still acting like it did but I honestly haven't seen anyone claiming it did in recent months. A new vaccine is needed for those wanting it. By now, case fatality rates are so low and almost everyone has some sort of immune response we are no longer dealing with a novel virus.
There's no perfect data out there, but...

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Again, it's true in the binary sense, of yes/no, that you can still get infected.

But in an analog world, you're still less likely. Just not as 'less likely' as it used to be.