I could be mis-remembering, but my take on the EU settlement scheme was that the person on it gets a temporary right to remain in the country for five years, after which time they apply for and get a "permanent settlement" and can remain without time limit. Applying for the temporary right was an extremely simple process when my daughter and I applied. I believe the second, "permanent" process is pretty much the same. (I seem to also remember getting info that if I had been working full-time, I could have applied for the permanent option after only 3 years and then retiring.) They may have twiddled with the agreement, so you might double-check the current regulations.
What you would do related to getting her Irish citizenship wouldn't really matter, I don't think, to the EU settlement scheme, other than if she becomes an Irish Citizen she might have the option to change from the dependent of an EU citizen to an EU citizen in the scheme's classification system.
If she becomes an Irish citizen, as things stand now, the EU scheme would be redundant because of the free travel/living/working arrangement between the UK and Eire. I would stick with the first option (EU Settlement) anyway, since the UK could at any time decide "No Irish Need Apply". And, yep, the waiting period for Irish Citizenship is horrific - we've been waiting for a response since 2018, and what I see on the various Irish Citizenship boards indicates that's not terribly unusual, although married spouses seem to get approved a bit more quickly.
(Of course, the UK could also back out of the EU settlement scheme provisions, too, but I would think that unlikely. Although one can never really tell.)