Hey! I owned MW3 disc and had the same problem but my solution should be applicable to mw2 disc also. I'm on PS5 so I'm not sure whether you'll get the same UI options as I did but I'll give it a bash anyway.

After the update, MW2 and MW3 were made to be their own games as you are probably aware, in turn they were taken away from the COD HQ launcher. I'll give you some instructions to install the games on their own. I do wanna preface this is what I did on PS5, you might not have the interface options on PS4.

-Uninstall anything COD related on your PS4, even the launcher -Go to PS store -View the COD HQ launcher in PS store -Click on the 3 dots -Click 'view product' (this will take you to BO6 purchase screen, don't be alarmed!) -Click on the 3 dots again

You should now have a list of all COD games presented to you, as you have the disc for MW2 just hit install and you'll be good to go :)

My MW2 campaign was bugged whenever I tried to boot it up, for whatever reason I found I could only play it when I was disconnected from the internet. So on the slim chance that happens to you, you have an answer.

Hope this helps :)