There are so many varying opinions on hamster care, and even contradicting ones on youtube videos. It's partly why we have policies and guidelines on various things on the forum, after consultation, and try to keep to authoritative or verified resources on here - but water bottles and bowls is not included in policies and guidelines.
It has become more popular for people to use a bowl these days, without issues. As with everything, care is needed as to the size and shape of the bowl and where it's put. One concern about them is if the water gets contaminated. Unfortunately some people might put them on the substrate and them get substrate, poops or food in them eg. Or they may not replace the water often enough. Or not notice if the bowl is empty if tipped over (although the latter two could apply to bottles too!). So as with everything, it's about taking care with things.
I still use bottles - I use the 75ml ferplast drinky ones which come with a useful bar attachment so they're very easy to take in and out of the cage and the spout is on the inside of the cage, not poking through the bars. They're the only ones I've found that don't drip and are reliable at letting water out IME. Although the classic ones are popular too. There are dangers with bottles too in that they may block or stop letting water out. So a daily check of a water bottle is important too - tapping on the spout to check water is still coming out.
I'm still on the cautious side with this and am quite happy with my bottles! Having them at the right height is important. But I know people are happy using bowls as well. A hamster getting wet is never a good thing but I think that would only happen if they happened to fall into a bowl accidentally. So as with bottles, it comes down to the right place to put them probably. I would think a shelf and not directly on the substrate.
As Erin's video says, both have their pros and cons
These are the Feplast drinky ones. I have spares also in case one stopped working. I think it's probably important to always have a bottle around if needed. Eg if you went away overnight.
These drinking bottles for small pets are suitable for all kinds of wire net cages thanks to the practical hook they are provided with. The stainless steel nozzle with globe valve ensures a perfect watertight.
www.portonaquapet.co.uk