It is not even a separate expense for me, as I just use my running shoes as my regular shoes. Also, maybe it is my gait or my lack of weight, but I estimate my shoes last 1k miles.
I started running fairly casually but eventually started doing marathons. I run about 110 miles a month so I'm switching out shoes every 3 months. My feet suck so I'm also replacing a pair of orthotics every 2 years. I got a full set of summer and winter running gear and enough of each to last me a week. I also have a hydration vest, a GPS watch (not necessary but very useful), a set of Aftershokz bone conductive headphones so that I can listen to music while maintaining situational awareness, a pair of good sunglasses specifically for running (I sweat a lot and would not want to ware the same pair for everyday use), I have a few soft flasks that go in my hydration vest, and I've had to invest in a pretty decent treadmill to run on during the worst parts of winter.
Not everything I've listed is 100% necessary but as with most hobbies it finds ways to become expensive the more dedicated you are to it.
[*] That's true where I live (northern Europe) for pretty much all of my runs up to ~20km. In hotter or sunnier climates it may be necessary to carry water for shorter runs and/or put on sunscreen.
It is recommended anytime you are outside when the sun is out.