OK, this sounds like it might have to do with permissions and security in Catalina. Catalina is VERY "possessive" about itself. VERY. Consequently, it may be refusing to install some of the necessary "extras" needed by DI and that's why you may be getting the "the developer cannot be verified" messages. Basically, Catalina only wants to install programs that come from the Mac App Store or from "certified developers". Personally, I find that intrusive as I consider my computer to belong to ME, not Apple, and I should be able to do what I want with it. I get that Apple are trying to "protect" it's basic, novice "user" but sometimes they can be a bit "heavy-handed" with their security measures.
Fortunately, you can "regain" control of your machine with some simple steps.Doing this does, however, put you, theoretically, "at risk". I hate that phrase because it is used deliberately to scare users into NOT gaining full control over their machines and is also, IMHO, very patronising.
My guess is that, if you used wine in the past, then you are aware that installing software from "unknown" sources DOES have potential risks to your system.
However, I also guess that you are VERY able to make an excellent judgement as to what "non-Apple" software you are going to install on your machine.
So, having said all this, you can make "non-Apple certified" software installable by following the following steps. (I have done this on my system and it makes my life SO much easier)
(This article also shows you how to reverse the process so that your machine is "locked down" again to Apple Apps, should you decide to.)
So, if you follow those steps from the link and then go to System Preferences/Security & Privacy/General tab ... you should have this :
... with "Anywhere" selected.
Now, you also need to allow Crossover to access certain things on your computer, so now, click on the Privacy tab and ensure Crossover has a tick in these places:
(you may not have all these options for Files and Folders, depending if you have used Crossover to install other applications besides DI)
NOTE: You do NOT need to give access to Crossover for Full Disk Access even though Crossover appears in it's options.
OK, so now, Crossover has the ability to install correctly. I suggest at this point you delete any bottles you made for DI and create a new one using the standard XP bottle option.
My next question is: Your downloaded GoG CC installation file - is it on your desktop? If it's on an external disk I suggest you move it to your desktop to create the bottle.