I'd be wary of latching onto tea and fixating on it as a miracle cure for anything, although there is no doubt that it is good for you and has many valuable health properties associated with it.
But that's perhaps the point, many foods have health properties. My view is that they work best when eaten/drank with other foods. What I mean by that is that rarely do the healthy properties of food work alone. For instance, if you wanted to take vitamin C, you're probably better off eating an orange rather than focusing entirely on just ingesting vitamin C through a supplement. This is because the white orange pith contains bioflavonoids which boost the action of vitamin C.
Green tea certainly has antibacterial properties (my husband is convinced it helps him ward off sore throats) but then so does wasabi, so does ginger, so does daikon, so does umeboshi, vinegar, miso and quite a few other foods common in the Japanese diet. If you go to Korea then you will probably have tea with kimchi, another food with powerful antibacterial properties. (The Koreans take 'medicinal food' very seriously, by the way).
Personally, I think it's best to eat a balanced diet. If you subscribe to the theories about food and health then you might like to try eating and learning about traditional foods, usually there's somewhere in the world where incidents of a particular health problem are particularly low... the diet of this region is usually the key reason. But you'd need to fully immerse yourself in this diet - taking out just one aspect of it rarely helps.
As I said, there are tons of foods with proven anti-bacterial properties. Nothing wrong with deciding which ones you like and having lots of them... green tea with kimchi and rice, tea sweetened with high grade manuka honey and ginger cake/ginger preserves, konbu kelp tea with lots of umeboshi, miso soup with daikon, Korean honey-ume tea or honey-yuja (or yuzu) tea. The list and combinations must be endless.
I hope your search for natural anti-bacterial remedies is pleasurable and not a chore.
(for diabetes you might like to look at buckwheat - both the noodles 'soba' and the tea - also called soba cha - or sobacha そば茶
Again, this would be just one of many potential foods to adopt in a diabetes managing diet)