A dell support article link follows with a great deal of information on batteries and maintaining long life.

https://www.dell.com/support/article/sg/en/sgbsd1/sln128667/laptop-battery-faq?lang=en

just what are the different modes in DELL doing? and which one is the best?

In my experience, extending the useful life of a laptop battery depends on so many factors that it will always be a moving target. That said, I always set my laptops to "Adaptive". I guess just to let the computer figure it out!

I have found very good information and knowledge at this site (Battery University):

https://batteryuniversity.com/

There is NO best!

It depends on the age of the battery, the manufacturer, the ambient and work temperature, the use load, the charging cycles and on and on.

If you read the documentation provided in the links above you should arrive at your own conclusions.

How exactly does the "Adaptive" mode behave?

Dell's definition for Adaptive Mode:
"Automatically optimizes battery settings based on the user's typical use patterns. Recommended for user's who want to "set and forget"."

Basically the laptop uses algorithms to achieve a best case scenario charging pattern for your laptop.

How does it work "exactly" is an unknown quantity. An equation with too many variables.

that is, it can top up to 90% by tipping that it is 100%?

i think primarily ac use is a good option as it uses power from ac adapter when connected

I have mine set to custom, and start at 85 and end at 90. works best of all of them since I need runtime but i use it docked too. the other ones don't do much as far as health goes. 80-85 is better for new batteries, mine is at 73% health since its refurbished.