Do I need an Irish transit visa to connect to Dublin in the UK? (Saudi passport and British visa)

I am a Saudi passport holder with a permanent residence in the United States and would like to book a Washington-Edinburgh flight with a three hour stopover in Dublin. I know that there is a joint travel agreement between the Republic of Ireland and the United Kingdom. I was wondering if I needed an Irish transit visa to connect to a Dublin-Edinburgh flight, or if a visa in the UK was sufficient. And are there any users who have traveled US-RoI-UK under the same circumstances with the need for a UK visa who can share their experience? Users who are not visa-free for the UK or Ireland, that is to say.

From what I've read in these forums and in others, it seems that Irish immigration controls unofficially on behalf of the British government.

I have also heard concerns from people claiming that Aer Lingus employees could deny me boarding based on an employee's confusion when looking for the terms and conditions. visa required for TIMATIC.