Am I supposed to have access to "com.apple.TCC"?

Apparently the TCC database stores the "privacy database": settings from System Preferences > Security & Privacy > Privacy.

See https://eclecticlight.co/2017/01/09/controlling-privacy-in-macos-sierra/ and man tccutil.

The article says

... this is managed in a special TTC database, which is stored in the folder ~/Library/Application Support/com.apple.TCC. There is also a master database stored at /Library/Application Support/com.apple.TCC, but you cannot open that folder, as only the system has that privilege.

On my iMac running High Sierra:

$ ls -ld /Library/Application\ Support/com.apple.TCC ~/Library/Application\ Support/com.apple.TCC
drwx------  3 root    admin  102  4 Oct 11:15 /Library/Application Support/com.apple.TCC
drwx------  3 ashley  staff  102 29 Jun 16:13 /Users/ashley/Library/Application Support/com.apple.TCC

Note the different ownership: the one in /Library (= Macintosh HD -> Library) is owned by root, and the one in my home folder (~/Library/Application Support = /Users/ashley/Library/Application Support) is owned by me. Because the permissions are drwx------ in both cases, only the owner can see into the folder... so when I look in Finder, the one in /Library has a "no entry" sign on it (because I'm not root), but I can open the one in my home folder, and see there is a file there named TCC.db.

I don't know why you see a difference between your MacBook Air and your iMac. In older times, I'd recommend you "repair permissions", but I believe that facility has gone away in the recent operating systems.