Both have different use-cases so I don't think Digital Dollar will be a threat to bitcoin or vice versa. Bitcoin caters to the ones who want to save their money from inflation and/or are looking for peerless transaction across countries and borders with minimal to no trouble. Digital Dollar I suppose will be exclusively used as a form of online payment much like how digital payments are made today, only except you may need to top up or something in order to get a hold of it.
The banking system is behind most of the cryptocurrencies. They want to familiarize us with crypto, it is the first step to make us accept the CBDCs, which was always the plan. I already hear many crypto libertarians saying: "I use USDT because it's more convenient, the value is stable"

I guess you are totally wrong on this statement of yours, because the banking system has never been behind any cryptocurrency, nor owned any cryptocurrency. But if what you meant is that banks are behind all Central Bank Digital Currency "CBDC" just like the digital rupee & E-naira, then it's agreeable, because there is a huge difference between these two.
CBDC are the digital form of a nation currency built on the blockchain to enable easy transaction, controlled by its central bank and the government. And secondly, USDT is not a CBDS but a stable cryptocurrency pegged to the American digital dollar
Matey couldn't be any farther from the truth. Most cryptocurrencies in the market aren't regulated by any central authority which is why some superpowers like China are opposed against usage of it. And even if they do want to familiarize us with crypto because they are behind it in the first place, I don't see the point of creating another currency instead of just backing the biggest cryptocurrency in the market right now.