Regarding the bolded — the best team certainly wins the regular season more often than the tournament, but I wouldn’t go as far as “pretty much always”. Look no further than the Big Ten this year, where it’s entirely possible Purdue will lose the regular season title to Wisconsin but win the Big Ten Tourney title. Illinois in 2021 was arguably the same (arbitrary choice of win % over W-L notwithstanding).
KenPom wrote a blog post back in 2010 about the same topic. That year, 18 of 31 conference tournaments were won by the conference’s best team. Regular seasons were better, but not much: 21 of 31.
Would be interested in whether anyone has seen any data over multiple seasons, and perhaps considering shared titles.
Oh, and major disclaimer - as much as I enjoyed the BTT title last year, I would MUCH rather win a regular season championship!