In Draw, F4 does open Position and Size.
In Writer/Calc that would be convenient too.
For an image in Writer, F4 should open tab Type of the dialog Image (properties)
Currently F4 does nothing in this situation.
OK -> NEW
Proposed patch for Writer: https://gerrit.libreoffice.org/c/core/+/108883
Objection to use a precious function key for a secondary command. They are typically reserved for global features such as Help/F1 or Rename/F2.
While P&S might be crucial for Draw it's not for Writer/Calc.