This may prove difficult as the catholic church is dogmatically committed to the special and irreproducible nature of the human soul. Any framing intended to align with them would have to exclude any kind of mention of AI sentience, I'd say. Perhaps a strategy might be to use the angle that AI may seem even if it is not, and that therefore protections for Digital Minds are also protections for those who have become attached to them. This might not be too persuasive, however, as they may insist on breaking that attachment instead.
On the Pro-Human AI Declaration. The intent seems, to me, to avoid creating sentient AI. I do not think that, if such AI ended up coming into the scene despite efforts against it, that they would be obliged to reconsider their position on personhood.
On the potential effects on the Catholic population. I study at a Catholic university and all of my professors already had these same thoughts well before the new Pope. I don't think these positions are particularly novel among Catholics. The encyclical might extend the reach of these ideas, but I'd be more worried about your second point than the first.
Who holds the power, who stands to benefit, and who is disadvantaged by any given decision are crucial considerations that the suffering-focused approach seems to miss. This is a good framing, and key to showing how this issue is not just ethical but political as well. In fact, by the time we have morally significant AI, it is not implausible to think that there will also be means for inserting desires, beliefs, etc. into a human mind, or designing human babies to specification, fixing their roles and life paths before they are even born. Who is to stop those in power from doing this to us? How are we to advocate for our own cognitive liberty and morphological freedom if we are not willing to grant it to AI?