I myself am on the fence about overpopulation. But just assume it’s true. How would the Church deal with it?
Population swings. Currently, both the US (and can’t speak for Canada, but my guess is that it applies) and Europe are either teetering on the edge of replacement or are well below it; some countries in Europe may be irreversably below it unless they start having large (as in 4 kids or more) families.
And in fact it appears that other large areas throughout the world are on a down swing. The UN estimates are that population will continue to grow; but there are numerous studies indicating just the opposite.
China, for example, has pursued a “one child” program; but coupled with that and not spoken of widely is that their population has been skewing to a better than 50% male, and fewer females; and there have already been questions asked as to what that will do, with concerns of either in-country destabilization or possibly resulting in was, potentially with other countries.
The US fertility rate in 2018 was 1.8 children per woman; replacement rate is 2.1; and the 1.8 rate includes immigrants (particularly Hispanic, which tend to larger families).
The overall rate then was 2.4 children per woman; but countries with the lowest birth rates include Poland, South Korea, Bosnia and Herzegovina, and Japan. Taiwan had an average of only 1 child. Both Africa and Afghanistan are in the 4 to 7 child range per woman.
Aleteia has had several articles on the matter; and the best evidence appears to be coming from Lancet.