I'm having the same problem. iPhone 12 Pro Max, iOS 14.3 synced with an M1 MacBook Pro with macOS 11.1. Everything works perfectly on the iPhone. If I connect to the Mac using the included USB-C to Lightning cable, "Trust" this computer, and do a "Sync" on the Mac, all apps on the iPhone will no longer launch. They'll display the initial splash screen / loading screen, then immediately terminate. This includes Apple apps like "Apple Support" or "GarageBand". However, built-in apps like Messages, Settings, Find My, etc., continue to work properly.
Uninstalling and reinstalling the apps shows the behaviour you mentioned. The app icon shows up greyed out and fails to install. Installing new apps also fails with a greyed out icon and will not install. Offloading the app and trying to reload it gives a grey icon and fails to install.
The only work-around I've found so far is to "Erase All Content and Settings" on the iPhone, then restore a backup from iCloud. This resolves the problem on the iPhone until I try to sync again, at which point the problem comes back.
Digging into the iOS logs with Configurator 2, I found the following:
Dec 18 21:46:04 Ricks-iPhone-12 kernel(IOTextEncryptionFamily)[0] <Notice>: AppleFairplayTextCrypterSession::fairplayOpen() failed, error -42017
Dec 18 21:46:04 Ricks-iPhone-12 SpringBoard(SpringBoard)[532] <Notice>: [Main] dispatch event:<SBInsertionSwitcherModifierEvent: 0x283e8b960; type: Insertion; intoIndex: 0; phase: DidUpdateModel; appLayout: <SBAppLayout: 0x283761880; primary: com.autodesk.ios.SketchBookPro3; environment: main>>
Dec 18 21:46:04 Ricks-iPhone-12 CommCenter[562] <Notice>: #I FBSDisplayLayoutUpdateHandler: update start
Dec 18 21:46:04 Ricks-iPhone-12 runningboardd(AppServerSupport)[502] <Notice>: <OSLaunchdJob | handle=56FA402D-780B-411F-B15E-C19E55A4E27C>: submitAndStart succeeded, state=3
Dec 18 21:46:04 Ricks-iPhone-12 CommCenter[562] <Notice>: #I FBSDisplayLayoutUpdateHandler: app <private> (UIApplicationElement 1 hasKeyboardFocus 0)
Dec 18 21:46:04 Ricks-iPhone-12 runningboardd(RunningBoard)[502] <Error>: Process start failed with Error Domain=NSPOSIXErrorDomain Code=12 "Cannot allocate memory" UserInfo={NSLocalizedDescription=Launchd job spawn failed with error: 12}
Dec 18 21:46:04 Ricks-iPhone-12 runningboardd(AppServerSupport)[502] <Notice>: <OSLaunchdJob | handle=56FA402D-780B-411F-B15E-C19E55A4E27C>: remove succeeded
Dec 18 21:46:04 Ricks-iPhone-12 CommCenter[562] <Notice>: #I <private> request: <private>, expects reply.
Dec 18 21:46:04 Ricks-iPhone-12 runningboardd(RunningBoard)[502] <Error>: Launch failed with Error Domain=NSPOSIXErrorDomain Code=12 "Cannot allocate memory" UserInfo={NSLocalizedDescription=Launchd job spawn failed with error: 12}
It looks like something is causing the FairPlay encryption to fail, which is causing the apps to not be able to allocate memory. Something with syncing to the M1 Mac seems to cause something in iOS fail.
Out of interest, I tried syncing the M1 MacBook to an old iPhone 6 running iOS 12.5 and it doesn't appear to have the same issues.
Until we get a fix from Apple, can you try resetting your iPhone/iPad and just use iCloud or the App Store app and avoid syncing with your Mac Mini until the issue is resolved?