tl;dr - 2 doses of Pfizer (and presumably Moderna) will provide almost no protection against infection, but hopefully still good protection against severe disease or death.
2 doses plus an infection, or 3 doses, ought to provide pretty decent protection against infection at least for now, but may wane.
An Omicron-specific booster will be a very good thing. Sadly, it's looking like that might be March before it's available in huge quantities, and my guess is we'll be in Omicron City by the end of January.
We still have no real idea if Omicron is more deadly, less, or the same as Delta. All the discussion about "it's less severe" is based on the thinnest hint of data. More data soon.
What about 3 doses and an infection?
You get a COVID toaster as a hard-earned gift. If you stand near an infected person, you should be able to hear their viruses screaming in terror at your presence.