It's expected for Tether to print when the crypto market cap is growing, because most crypto trades in USDT. So you cannot reliably say what is the cause and what is the consequence here.

Then, if the price was pumped and the liquidity didn't match it, it'd be a perfect target to squeeze (because the market is so highly leveraged), at least one trading firm should've attempted it.

But they rise by perfectly round numbers and mainly in response to falling prices

What do you get by squeezing bitcoin? Once the liquidity is exposed as non existent everyone loses their money. There’s no hedge