Apps not recognised as installed by App Store or findable by Spotlight following Migration Assistant?

I installed macOS on a new SSD in my MBP and during setup I used Migration Assistant with a Time Machine backup (because it wouldn't let me do a full Time Machine restore).

Most things seem to be back to normal except that Spotlight is not finding some apps that I definitely have installed (like Pages, MS Word, Xcode, etc) and the App Store doesn't realise that these apps are already installed.

It only seems to be an issue with apps that I got through the App Store. Apps I downloaded through Adobe Creative Cloud like Illustrator, InDesign, and Photoshop both show up in Spotlight and work fine.

What do I do? How do I fix this?