That window doesn't have any direct connection to the Automation designer, but you could probably make it happen with the other actions.
It's Oracle that generates those reports, not Toad. We just send the command to Oracle and then pull the result.
So, for the AWR Report, for example, if I turn on Spool SQL when the report is generated, I see this output:
Select *
from table(dbms_workload_repository.awr_report_text(
2877469868, -- DBID (Not going to change)
1, -- Insatance ID (Not going to change)
2818, -- Starting snapshot (will change)
2973, -- Ending snapshot (will change)
0)); -- Options (not going to change)
So if you came up with a view where you could select the starting and ending snapshots that you want, you could change the above select statement to get those values from your view, and then put the select statement in an "Export Dataset" action and export to a text file, and put that in the automation designer.