Why are the cinnamon sugar bagels I buy becoming so wet

I've never seen the kind of garlic bagels spiceyokooko is talking about, but I am familiar with garlic bagels of the variety you're referring to. I don't usually make garlic bagels at home because I'm happier with simpler ones, but I have made some ages ago.

I've usually found most things stick just fine to recently boiled bagels, but for fresh garlic, you may find it more reliable to brush an egg wash (roughly equal amounts beaten egg/water) on the top of the bagels before sprinkling on the chopped garlic. That'll work almost like cement to keep most of the garlic in place after baking.

There's some possibility that the level of moisture in fresh garlic may make it harder to just press the egg-washed bagels into a bowl of chopped garlic, as you would likely do with seeds.

Also, I wouldn't expect that all of the garlic will stay stuck. But with the egg wash, most of it will.

As for the texture of the garlic, there's a pretty wide range of common results at the variety of bagel shops I've tried in my life; some are golden brown and some are near burnt. That's a matter of cooking time, mostly, but also the starting moisture content of the garlic.

I would expect that most bagel shops use bulk, pre-minced garlic so that they can save on a little labor. This is typically a bit drier than if you fresh chopped the garlic at home. Consider buying the prefab stuff and see if that gets you closer to what you want. If it does, and you prefer to do the heavy lifting on your own, mince the garlic and let it sit on the counter to dry a bit.

Another strategy altogether is to mince garlic and mix it with some oil, and smear it atop the boiled bagels with your hands. I think this should stick reasonably well, and will affect the texture of your result.

Since I'm not 100% sure what your platonic ideal is for the garlic texture, I can't say whether the oil-mixture or egg wash route is going to be a better choice, or some hybrid, but those are some options to explore that I think will get you closer to your target.

The main purpose of adding things to the boil are to promote browning and flavor. The texture of the crust is more a product of gelatinizing the starches by boiling, using a high oven temp, and using a good amount of steam during baking.

You can increase browning two main ways, by promoting the Maillard reaction and/or promoting caramelization. Baking soda, lye, or sodium carbonate baths increase the Maillard reaction, and increase surface gelatinization by breaking down some starch, but also give the bagels a "pretzely" taste. You can also promote the Maillard reaction by adding protein to the surface by using an egg or milk wash. Sugar (white or dark), honey, and malt added either to the boil and/or the dough increase surface caramelization and also lend a subtle glaze.

Personally, I always use malt incorporated both into the dough and into the boil. It adds a subtle sweetness and cereal flavor that complements the bagels. I find the pretzel taste from an alkaline bath off-putting. When I don't have malt I use honey, molasses, or brown sugar. I don't use an egg wash either, if you want to add toppings just place the bagel into the topping right out of the boil... they'll stick without anything else.