Issue
'Conflict Status' & 'Conflict last run' fields are not getting updated on Change record until after the record is reloaded.
Cause
Conflict of timing
Resolution
We confirmed that its just a timing issue and adding delay will fix this. As long as you don't have any issue with adding a bit of delay then it should be fine.
In testing, we added below code into the ChangeConflictWorker Script Include within the start method.
//adding some delay to try and fix live update not coming when the form loads.
gs.sleep(5000);
You may want to try some other method of adding this delay or make the process synchronous and the code above is just a way to demonstrate that the issue is caused by a conflict of timing and shouldn't be considered a solution unless the you decide to add that based on your own assessment of the situation.