Write final README.md

[goloroden]

What is this task about?

Currently, the README.md is not aligned with the appropriate files of the other client SDKs, but only contains a rough overview of what this SDK does. We should change that.

What needs to be done to complete this task?

• Copy the README.md file from the Go client SDK
• Adjust the code examples
• Adjust the wording, where necessary

[Snapstromegon]

@dotKuro just to note:
If you include code examples in the README, right now they will become integration tests / doc tests for the crate. This has some benefits and downsides:

Benefits:

• code is automatically run as tests, so CI checks that the code is valid
• readme and its examples look the same everywhere

Downsides:

• It's possible to hide lines in doc tests (I use this quite often in the existing ones), but github (and I think crates.io) always shows them

Overall I think we should investigate if separating the readme from the crate doc's entrypoint would be a good thing to do (so not include readme in the crate as doc, but write a separate one in the lib.rs).