The warning signs have been there for a while that mortgage lending rates were about to rise. Central banks around the world, including the European Central Bank, have been indicating that they will increase their key lending rates for banks.
No, BOI don't give any cashback with their green rates or high-value mortgages, and existing customers can't switch to those products, so the "double switch" is not an option.
Edit: it seems that non-BOI customers do in fact get cashback when they switch to a BOI green rate provided that it is not also a high-value (>€250k) mortgage.
There is a strategy similar to the Haven one with EBS (see @Brendan Burgess's third post in this thread), but it is higher risk in the sense that you will be stuck on a 2.9% rate if they don't allow the second switch.