Well ladies and gentlemen, here is the promised feedback:
This morning I purchased an iPhone X from O2 which is my carrier and they have a shop in a Town nearby. I have purchased all of my iPhones from them over the years (including those for my wife) and thought it best to try there first.
The Guru at the shop, an Apple man as it happens, assured me that Restoring the iPhone via iTunes would include all the apps.
Knowing that I had iMazing and iCloud as alternatives I did the following:
1. Connected to iTunes via USB and had to do an software update to 11.3 before I could Restore.
2. Then I Restored from my iPhone 7 backup. Took 3 minutes.
3. All settings correct. All apps restored.
4. I had to input my Apple ID credentials several times as I progressed. For Apple Store, iTunes, iCloud and for those apps that were linked to my Apple ID including Keychain.
5. As regards the apps. All apps spontaneously re-downloaded. I did not have to do anything to initiate this.
For some 60 apps or so, the process was complete in just over 5 minutes; during which time I was able to continue the set up process, activate Apple ID, Face ID, fiddle around with settings and so forth - i.e. the app re-download went on in the background.
I did not have to wait for it to complete to use the iPhone.
As I purchased the X from a shop, I had to phone Apple to buy AppleCare plus. They run diagnostics, get proof of ownership, serial number and so on. Finally, when chatting to the Apple helper, he confirmed that iTunes backups include all apps.
But he did admit that Apple had not made clear the distinction between no longer able to purchase/download apps via iTunes - but still being able to restore these from an iTunes backup.
Conclusion: It is possible to restore all apps from an iTunes backup. - as well as all the usual music, photos, data, passwords, health etc.
I truly hope this clarifies things for future members.
Ian