There is a lot to unpack in your question and a lot of it is political rather than legal. I have hyperlinked the relevant issues throughout for further reading.
You ask:
Is it for "constitutional" reasons ― the British government did not have the authority to extend the ban to Northern Ireland?
No. In the UK, Parliament is supreme. This means that they can, in theory, legislate on whatever they like and cannot be challenged by the courts on constitutional matters. Parliament can, and has, changed fundamental parts of the Constitution before and legally this can be done with relative ease (unlike most constitutions) due to the unwritten nature of the UK Constitution. The only concrete limits on Parliament's ability to change the Constitution are political (and there may be limits on implied repeal, but this isn't directly relevant to your question). In general, the UK Constitution is very different from most and its great flexibility means that many believe there is no limit to what legislation Parliament has authority to pass or repeal.
You also ask:
Is it for political reasons ― the British government deliberately did not extend the ban because they did not wish to upset the people and/or leaders of Northern Ireland?
Partly. Some powers have been devolved to Northern Ireland. This gives them some autonomy, but Parliament remains supreme and they can overrule anything they don't agree with. In 1998 a new Northern Ireland Assembly was created (after it had been abolished in 1974). As the handgun ban was passed a year earlier, in 1997, the extent of devolved powers was much more limited. The efforts to devolve power again meant that Northern Ireland would soon regain the ability to legislate on such matters, so it was of little significance to Parliament. Additionally, the political landscape in Northern Ireland was fragile due to The Troubles. As a result, the Police Service of Northern Ireland were responsible for handling licensing. If Parliament had attempted to legislate on such matters, it could have heightened political tensions further (if you are interested in why, HistorySE and PoliticsSE are better places to ask such questions).
Finally, you also said (in a now-deleted comment below this answer):
What I'd really like to see is the part of the 1997 act where it says the equivalent of "this ban does not apply to Northern Ireland".
This can be found in s53(5) of the Firearms (Amendment) Act 1997 (page 28) which says: "This Act does not extend to Northern Ireland." This is for the reasons explained above.
