blackcat8 I keep reading that the apps can't see anything from other apps installed unless given mutual consent.
I think the mutual consent wording it maybe a little bit misleading. Any app can set itself up so it can accept IPC requests from all other apps, even apps it does not know about. Any app can also make IPC call to other apps that have set themselves up to accept such requests, even apps it does not know about. It is not a very strict enforcement. "Intents" is how IPC is usually done between apps on Android, if you want to read more.
blackcat8 How would I know if apps have consented to communicating with each other?
As far as I know, there is no way to see what apps are doing IPC requests to other apps.
Many apps talk to Google Play Services, but it is rather rare for other user installed apps to ever talk to each other, since they are not coded to know about or depend on the existence of each other. The "Share" feature being the exception. Some apps do not allow IPC calls from other user installed apps at all.
blackcat8 Is it apps that have storage permissions or something else?
No. You cannot control this. There have been plans on adding an "app communication scope" feature, but for now, putting apps in separate profiles is the only way to make them not communicate with each other.
blackcat8 I'd like to set a up a profile where I can store all intrusive apps or apps that need to connect to a Google account, but I'm worried that dumping them all in a single profile would defeat the purpose if they're communicating with each other.
If they are all connected to the same Google account anyway, there is no point in preventing them from communicating with each other on the device, they are communicating through the cloud anyway. Usually it only makes sense to prevent apps from communicating with each other if they are connected to different e-mail addresses or phone numbers, and you don't want anyone to learn those e-mail addresses or phone numbers belong to the same person, and you don't want cloud data from them being mixed together.