Would be nice to have separate folders for the files in WRITER, CALC, impress etc. (Tried to go through “File an enhancement request”)
It’'s your computer, you can do whatever you want. Remember that separating file types within a folder normally requires only to sort by file type in a file manager. LO defaults to last place it saved something.
Given that most work is project-focused so that spreadsheets, documents, presentations, etc. relating to a particular project get put in the same project folder or sub-folder, it seems counter-intuitive to do it differently.
If you mean the so-called “working directory”, it can be reached in LibreOffice under Tools>Options>LibreOffice>Paths.
No, you can’t split it up by the LibreOffice modules.
As already written by @EarnestAl, you can e.g. create your own directories in the file manager.
In LibreOffice, you can then use the menu File>Save as... you can search for the desired file path and save it there.