To collect all the FM’s called by some application during the work I would use Debugger-Scripting.
Log of all ABAP commands of an application can be provided by script RSTPDA_SCRIPT_STATEMENT_TRACE
Drill down to debugging as usual, select the RSTPDA_SCRIPT_STATEMENT_TRACE
Check the box „Breakpoint reached“ and create new one on „CALL FUNCTION“ then start the script.
When everything will be done, /h into the command line, press F3 and then stop the script.
The transaction SAS can show the results: