How can I update a checkbox on the attributes tab when the sales category changes?

FieldVerifying is meant to be used to verify a value being saved and be able to cancel it under certain circumstances. Since that’s not really what you’re needing, I would use FieldUpdated.

protected virtual void _(Events.FieldUpdated<INItemCategory, INItemCategory.categoryID> e)
{
	INItemCategory row = e.Row;
	if (row is null) return;

Since you’re working in the InventoryItemMaint graph, you can use e.Cache.Graph to get the current graph instance and then grab the current InventoryItem from the graph instead of selecting again (although that would work).

var inventoryItemGraph = e.Cache.Graph as InventoryItemMaint;
InventoryItem item = inventoryItemGraph.Item.Current;
if (item is null) return;

Then, since you have the graph instance, you can just kindly request that your field be updated with the new value.

(I couldn’t tell from your code if you wanted this value to be true or false)

// Set the checkbox value
inventoryItemGraph.Item.SetValueExt<InventoryItemExt.usrAIBCCatAdded>(item, true);

Here’s the whole thing:

public class InventoryItemMaint_Extension : PXGraphExtension<PX.Objects.IN.InventoryItemMaint>
{
    #region Event Handlers

    protected virtual void _(Events.FieldUpdated<INItemCategory, INItemCategory.categoryID> e)
    {
        INItemCategory row = e.Row;
        if (row is null) return;

        var inventoryItemGraph = e.Cache.Graph as InventoryItemMaint;
        InventoryItem item = inventoryItemGraph.Item.Current;
        if (item is null) return;

        // Set the checkbox value
        inventoryItemGraph.Item.SetValueExt<InventoryItemExt.usrAIBCCatAdded>(item, true);
    }

    #endregion
}