Are there any specific rules for the pairing announcement, like they have to be announced "x" hours before the start of the next round?
Of course not. What you suggest is totally impractical. Let me give you some examples.
Next month I will be chief arbiter in a FIDE rated blitz tournament. There will be 9 rounds starting at 11am and finishing about 3pm. At the end of each round, once all the results have been entered into the system, the pairings will be done, printed and an announcement made for the players to check the pairings and find their board. Normally I will be able to start the next round within 3 or 4 minutes of the pairings being published. The idea of waiting "several hours" before starting the round makes no sense.
In a week's time the Four Nations Chess League, one of the main organisers of FIDE rated chess in England, is running a 5 round FIDE rated weekend congress. Here is the schedule of rounds:
Round 1 Friday 19.00 - 23.00
Round 2 Saturday 10.00 - 14.00
Round 3 Saturday 15.00 - 19.00
Round 4 Sunday 10.00 - 14.00
Round 5 Sunday 15.00 - 19.00
As you see on Saturday and Sunday there is a one hour gap scheduled between the morning and afternoon rounds. That means the pairings will be published less than one hour before the next round. With a 30 second increment if one game runs on for over 100 moves then that is likely to be much less than half an hour.