The IDE docking is based on TDockTabSet, which was introduced in Delphi 2005. It has received some attention later including Vcl styling. The only demo I could find is an old one by Jeremy North, but the source code is not available. Jeremy also seemed to have expanded this component in his QualityCentral client (look at the images at the end of the article), the source code of which is also not available.
It is not the sleekest implementation, but apparently it works OK in the IDE.
Agree in general, but it depends on the application. All the IDEs I know of, including Visual Studio, use docking extensively. Same is true for VS Code for example (but no floating forms though).
In PyScripter I use a heavily modified version of JvDocking (part of the JVCL library), but I am still looking for a better open source library. I may have to create one.