I just heard about Bitget today, and when I searched it, Bitget doesn't listed on my Ministry of Trade country, so I will avoid it.
The list you're referring to also doesn't include Binance afaik, so it is not the best list if you want to compare the "trustworthiness" or reliability of an exchange. Most of them need active registration plus an office in the country, so it is understandable that some big exchanges would rather 'ignore' it and just use a proxy to get customers from the local market (like Tokocrypto and Binance for example). Still, I've never heard anyone mention Bitget either, so their marketing is certainly lacking for some markets. CMIIW.
There's no way to verify any centralized exchange, trade Bitcoin P2P with other person is also need a trust since you need to make the person will send his coins when you've send your coins first. The only way is using decentralized exchange or P2P which act as an escrow.
Other than making sure we visit the right address and judge whether a statement is wrong or not (which includes many things, such as marketing materials), I also think it is hard to 'verify' an exchange. A better term is probably to look for reviews from other members, or try it with a throwaway account if possible before you decide to use it as one of your main exchanges. It is impossible to remove trust completely, but at the very least we should be able to control our funds even if the platform we use went bust. I don't think an exchange fits that criterion though.