How to 'Stop' Action to use Healing Brush in Image Processor?

Do it partially, every 50 files without batch. Open first part of files, play action that is going to stop (using stop item without dialog and continuation), brush on canvas, continue the action by assigned key that is going to save & close a file. Do the same on remaining 49 files, then open another part of 50 and so on.

Tip: to save a file without overwriting, create new document, start recording and save it in output folder. Stop recording. Such saving item won't be bound to any file, just its format and the folder it had to be saved in.

I wouldn't call it an "issue" as such, it was designed to work this way, just as the script from jazz-y is designed to work differently.

I have a script that allows you to work both in normal batch mode and to continue operations after stopping (you can set a stop either in the script settings or in the action itself - as convenient). To continue operations after stopping, you need to call the script again (for quick continuation, you can either assign a hotkey to the script in the menu, or write it to an action).

Advanced-batch

The code is terrible in places, I would like to rewrite many points, but I have no time to do it, however, it has been working in my studio for more than 2 years without any problems and, in combination with actions, allows you to completely replace the standard batch and image processor.

Unfortunately, there is no help file. Most of the functions are intuitive, something can be understood in the process of working with it. The way to solve your problem with it in this video:

It sound like your Action stop,  stops the Action and also stops the Script for you could use the healing brush on the current document.  After you used the healing bush. You were able to continue the Action by clicking on the Action Palette Play button  for the action was stopped position to the step after your stop step.   There is no way that I know of that a terminate script execution can be resumed. Restarting it would start the whole batch process  over again it would not pick up on the current after your resume actions play execution ends.

The first thing you did wrong was to have a batch processor include an action that has interactive steps.  That kills the automated batch processing humans intervention is required to continue the automated process.  The second thing you did wrong was you stopped the action and batch processor so you could use the healing brush on the current document.  You terminate the Image processor script. You ended the Batch Process.