I do not think that the FTX FUD is going to do any more damage than it already has done. What more could push down the price at this point? SBF not finding the investors who will give him billions of dollars to save his sketchy exchange? Everyone already knows that that will never happen. If I had to take a guess, I would say the FTX news has already done the most damage that it can to the price of Bitcoin. And that damage will be very short term. However I do hope people will be panic selling for a while longer.
Well, FTX will announce it's complete collapse, and while we pretty much already know that, people will still panic. However, it's not about FTX doing anything else, it's the time it takes for people to digest the news, and when the price isn't recovering in a week's time, people then start to panic sell, which drives the price down even further. I'm not saying that will happen, but it's a possibility. Then, if in two months time we're hovering around the same amount, then people will again lose faith. It's a vicious cycle.
However, the FTX news isn't exactly FUD so not sure why you're referring to that. It has happened, and it will effect the short term price of Bitcoin. Plus, the more this happens, the more reason the government will step in, and regulate the space further. Something which some people will see as a positive as it should reduce the risk of something like this happening in the future or others will see it as more interference. I guess it depends on what side of the fence you're.
Also, it depends on what you mean by short term. This will probably have an effect on Bitcoin's price for at least a couple of months. However, the grander scheme of things, Bitcoin will likely be struggling well into 2023 due to the other things that have happened previously to this, this is just something that's compounding more doubt on top.