Hi @gkallenbach,
Setting net-class copper clearance, copper width and drill size rules it is still possible just not from the Net Class Dialog anymore. The reason for this is that we have added support to handle all design rules the same way as well as support for scoping design rules for other objects apart from net-classes, such as: signals, components, signal layers, layers, object types, differential pairs and more.
In order to create net-class design rules you need to open the new Design Rules Editor by either clicking the button below or running the drc command from the CLI:

In the subsequent dialog:

click on Custom Rules tab and there you can define many types of design rules. Compared with the legacy behaviour the new design rules are split into categories and the ones you should start with are the: Copper Clearance, Copper Width and Drill Size. These are the rules that map to the Net Class dialog Rules tab. Because the new rules can handle scopes other than net-classes the UI is also changed substantially. Apart from scoping the new rules system allows for setting priorities, enabling / disabling, setting preferred value. Here is an example taht shows how to setup net-class Copper Clearance for net-class new-class:

Once you have selected the Copper Clearance category to create a new copper clearance rule you have to click the button labeled + at the bottom of the rules table view, please see below:

After you click there is a pop-up with 2 options: Different Signals and Same Signal you need to select Different Signals because this is what the legacy net-class rules useed to support. A new copper clearance design rule will be added that you can change as required:

After selection you get this:

You can update the Name, Minimum and Preferred values and Scope section is where you can define the net-classes for which the rule will apply amongst many other posibilities:

After selecting the In Net Classes scope for Object 1 which means that the rule will apply for any objects that are in net-class = new-class. Because the copper clearance is a binary rule (applies to 2 objects) you also need to do the same for the Object 2 scope. Then you can update the Minimum and Preferred values if you haven't done so yet. Once done click the Ok button and the new rule will be saved. If you want a rule to apply to more than one net-class then in the right-side drop-down after selecting the In Net Classes scope you can select multiple net-classes, please see below:

I agree that all these changes might look like a steep learning curve. Our goal was to create a unified design rules system that can be easily extended and allows for creating specific rules to target different objects or areas of the design (scopes).
I hope this helps.
Please let me know if there is anythign else I can help you with.
Kind Regards,
Constantin Popescu
Principal Software Engineer