How to transfer over €20k from BOI to another Irish Bank.

Unfortunately, the limits are a compromise between allowing large amounts to be transferred online v protection from scammers and hackers

If someone hacked your account and transferred € 100,000 to their account, no doubt you would be very unhappy.

Yes, having your branch call you is a work around.

My daughter needed foreign currency and left it very late to get it. She asked me for help.

I checked out my BOI app and it allows ordering of foreign currency.
When I tried to order it required 5 working days notice. This was after her departure date.

I rang BOI helpline. They could not confirm if my branch had sufficed funds in stock. They set up a call back from the branch.

Shortly after the branch called and confirmed they had the currency and reserved the amount I needed.