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.
Gabor Kelemen committed a patch related to this issue.
It has been pushed to "master":
tdf#107588 Assign F4 shortcut to Image Properties in Writer
It will be available in 7.2.0.
The patch should be included in the daily builds available at
https://dev-builds.libreoffice.org/daily/ in the next 24-48 hours. More
information about daily builds can be found at:
Affected users are encouraged to test the fix and report feedback.