Theoretically for labor you can go as far as to the minute per each named resource but this is not practical, some summarized data is better. But still it can be too much and what would be the benefit of doing so? You always will have the time cards for backup signed by the person who prepared each time card.

For equipment I doubt you will get time cards with to the minute/hour/day distributed to each activity.  In any case a monthly billing by your equipment division or equipment rental received after update DD.

For material, a distribution of every delivery at the activity level, the same.  I doubt you will get a distribution per activity of every single item that can be distributed among hundreds of activities.  The billing will be received after update DD.

Labor, equipment, materials are used on each activity intermittently and this adds further complication.

Accounting and Job Costing are designed to do this, scheduling software do not.  But Accounting and Job costing cannot do scheduling.  You need both systems, each shine at what they are best.

My hands down approach is to update execution time and remaining durations, assuming it was continuous unless a clear activity stoppage is known. Then allow the software to calculate whatever else was into the model based on the entered durations.

At home a small percentage of contractors have a good job costing in place and use a limited amount of cost codes [the same for all jobs] not thousands of activities codes unique for each job. Many have no job costing software and attempt to do it using the general journal accounts, not a good idea, but it happens!  Do not dream they will ever go to the complications a CPM Activity Costing would require.

We use the cost modeling of the CPM to model the future, for detailed tracking of costs we use the accounting system.

Good luck.