Gemini and Genesis are 2 completely separate entities. Of course this is with the assumption that Gemini themselves abide strictly by the regulations and licenses they were given, and not chut pattern like FTX. But this applies to all CEX, including Binance, CDC, Coinbase. If someone insists on committing fraud, there's no regulations, licensing or enforcement that can stop them.
For Gemini, they have this product called Gemini Earn, which is called Gemini Grow now. They stated very clearly that funds put in Gemini Earn / Grow is passed on to their 3rd party partner Genesis for returns. There are warning messages everywhere including when you want to deposit your Gemini funds into Gemini Earn. I used to put in Gemini Earn but withdrew everything after Luna collapsed. Once you put money into Earn, Gemini has no more responsibility for your money since the risks are now passed through to Genesis (and you). In hindsight, they probably should have just named their Earn product as Genesis Earn, and don't use the name Gemini since it gives the impression that it is an official programme by Gemini.
Gemini itself, if they abide by the rules which allowed them to operate, should be very safe, since they are a reserve exchange with 1:1 collateral, no margins, futures or derivatives. Of course, one can argue that FTX also say they are very safe but also collapsed, but I suppose Gemini's track records is a lot more solid than FTX. FTX wasn't brought down by their exchange itself. It was brought down by the actions of their management, which is fraudulent in the first place. FTX itself, if operated properly, is actually a massive golden goose, the amount they make from fees are ridiculous, which is why there are several big companies intending to buy out parts of FTX. I think the Winklevoss brothers should be more solid than that, they were already billionaires before starting Gemini, no need chut stunt.
I started using Gemini in 2017, rode through the 2018 bear, Gemini didn't let me down. After the FTX / Genesis news broke, I also withdrew my funds from Gemini, no issues at all. Recently I deposited a little back to buy / trade, and tested withdrawals. As recently as Friday, no issues too, funds were deposited and withdrawn quickly. I have a few wire transfers withdrawal initiated yesterday and today, Gemini processed it already, now waiting for it to reach my bank tomorrow / Tues since the US and SG banks don't process wires on weekends.