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In this video we can see the shulkers are shooting at a rate of once per second. https://youtube.com/shorts/8tUFaSZ4b7I?si=sszp4cnyXR4dXg9B The wiki confirms this but mentions a range of 1 to 5.5 seconds. I think this range is caused by the shulker closing and stopping shots for a few seconds but no longer than the max interval of 5.5 https://minecraft.fandom.com/wiki/Shulker#:~:text=The%20shulker%20continues%20firing%20every,unaffected%20by%20Levitation%20when%20hit