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Japanese bag policies are loose compared to US stadiums. In my experience, there are no restrictions on bag size or type, and professional cameras with big lenses are permitted.
Stadium employees at the entrance will search your bag, but politely ask for permission before doing so. If they look at your bag and then at you, as if waiting for a response, indicate they are welcome to peek inside your bag.
Ballparks have varying food and drink policies. You probably won’t be able to bring cans or glass in, but plastic bottles and food are typically permitted. Although the policy is being phased out, many ballparks let you bring in any drink—yes, beer, too—as long as you pour it into the provided plastic cups before entering!
If you encounter any unforeseen bag policies, please report them to me for future reference.