Overall, you are on the right track. I want to add that sucrose (table sugar) is made up of a glucose molecule attached to a fructose molecule. One of the things saliva does is to separate the glucose from the fructose.

Fructose is the main sugar found in fruit (thus its name). It isn't correct to uniformly say fructose is bad for you. It's the type of sugar people mostly consumed before sucrose became available.

Here is a reasonably reputable link that describes everything in more detail

https://www.healthline.com/nutrition/sucrose-glucose-fructose#absorption-and-use

At the bottom, they talk about how the presence of glucose increases the rate of fructose absorption, which is likely to be the actual problem, as opposed to fructose itself.