How to manually update a record during the process of a service catalog item?

Inputs can never be updated once the Service Request is submitted. This is by design.

For what you're wanting to do, what I would recommend is creating a Task and assigning it to the technician who should be modifying the field. The Task is just a reminder and acknowledgement that the action must be done, but the technician will still be responsible for manually changing the field.

Now since I just said "Inputs can never be updated once the Service Request is submitted.", you might be thinking, "How can they change it?"

In Setup>Service Desk>Dynamic Form Rules you can apply a form to the Service Request that will appear after the ticket is submitted. Those fields will show up under the Details tab of the Incident record. There, a technician can modify the fields that are applied using the Dynamic Form Rule.

 I have finally set up a dynamic form rule and a custom field. The problem I see now is that when I modify the custom field during the process, the condition sets I have in the process relying on this custom field, do not recognize the updated value causing the condition set to fail.

Any insight on why this is occurring or what must happen to ensure the condition is set to see the most current updated value?

Without being in the account or seeing screenshots, this is my first thought. Try looking to turn this on and see if it helps fix the issues.

Setup>Global Settings>Service Desk Settings

Just-in-Time workflow processing

Without being in the account or seeing screenshots, this is my first thought. Try looking to turn this on and see if it helps fix the issues.

Setup>Global Settings>Service Desk Settings

Just-in-Time workflow processing