I am not familiar with the way the Nextion official library works, but it does not surprise me that you ask about reading something from the display 'all the time'. You need to save the value you get from n5 in a static or global variable so its value is not lost when you change pages, and use the value of that variable to control the blink.
This:
const long interval = (60/rateSet*1000)/2;
Can't be right because 'const' means 'constant', i.e., unchanging. I'm surprised the compiler does not throw an error for that.