Make "Export Selection…" Actionable.
The fact that "Actions" is not in the list is telling.
Make "Export Selection…" Actionable. Currently, it is not recognized when recording an Action of when "Adding a menu item" to an existing action.
Actons, in general, are in dire need of attention in Illustrator. Please consider making them a priority.
Export Selection command can be assigned to a hotkey... it can be inserted into an action with the 'Insert Menu Item' from the Actions panel’s flyout menu... but this won’t be a full automation, you’d still have to verify settings and click OK.
But Export Assets / for Screens dialog now supports user defined presets, which can make it less tedious to setup. Does it solve the problem at least partially for you?