Update: Actually I successful entered Ireland on 5th of August (direct flight from Paris to Dublin) with my valid and used UK visa. The immigration officer gave me 90 days of stay. So actually if someone has entered UK at least once, they he/she avails the Short-stay visa waiver programme can go to Ireland from a third country instead of the UK.
I'm a Chinese citizen and I have a valid UK standard visitor visa for 6 months till October 2022. I've been to the UK (London) in May 2022 and went back to Paris where I live for the moment. I plan to visit Dublin in August 2022, do I avail the Irish Short-stay Visa Waiver Programme? If so, can I book the flight directly to Dublin or I have to enter the UK first then flight to Dublin?