How to report STA (Timing Analysis) just post-Synthesis but before P&R (Placement and Route)?

Nope, you can refer to https://www.intel.com/content/www/us/en/programmable/support/support-resources/design-examples/design-software/tcl/auto_processing.html

It is actually the same like the example above by not using GUI. Any reason that you need to use gui to automate the process? Usually, the solution is not using GUI for scripting purposes.