The trouble is that the blurb about green tea does not state how much it may affect insulin sensitivity. One would expect that if it had a spectacular effect they would have made some extra-concentrated extract of it.
From health.harvard.edu Health benefits from drinking tea, My take on tea (that from the Camellia species) is that imbibed in moderation it has a number of anti-oxidants in it which seem to be of help to our bodies. And that it has been consumed for centuries. The usual teas contain caffeine which is a plus or minus depending on whether caffeine causes too much stimulation of the heart beat or affects sleep. We cannot be absolutely certain if it is the properties of tea or the kind of people who tend to drink tea or a mixture of both that explains its apparent benefits.
Adding milk to tea is said to adversely affect the anti-oxidants in the tea. see npr.org/sections/thesalt/2012/09/27 - Health Benefits of T: Milking It or Not?
Most of the hype about tea and diabetes seems to boil down to that the ingredients may be beneficial but I could not find any solid research to prove how beneficial it may be.
But note that caffeine can cause release of glucose from the liver or sometimes a lowering of blood sugar (mayoclinic.org - Caffeine: Does it affect blood sugar?.)
For a comparison of how much caffeine is in coffee vs black tea or other types of tea: please see tealife.com.au July 2017 How much caffeine is in tea and which are caffeine-free? This will help with calculating the 200 mg caffeine amount referred to in the article above - mayoclinic.org. There is less caffeine in white than green than black tea.
Of course staying away from sweetened tea is best for one's diabetes and dental health.
Herbal teas are usually caffeine-free. There are concerns that some herbals may contain naturally occurring substances that may promote cancer (ncbi.nlm.nih.gov Risks associated with consumption of herbals teas - Mantiega and Park 1997).
Some herbs can interact with medications, or cause upset stomach, liver upset etc (stylecraze.com 10 unexpected effects of peppermint tea.)
Unborn children may be more sensitive to some chemicals so ensuring that a beverage is safe during pregnancy is also an important thing to find out for those of child-bearing years (see babycentre.com.au) and apparently if you are allergic to pollen you may be allergic to chamomille.
Personally I drink coffee x 3 in the day with milk as that seems better for my stomach ( any more than that, or taken later than about 4 pm I do not sleep well.
At night I like roobios tea, as it is caffeine free and tastes pretty close to black tea. However, I may mindful that Roobios is not without its problems (tealy.com.sg What are the risks and side-effects of Roobios tea?).
Each to his or her own.