IMO, when billing hourly, it should only be focused work. They aren't paying for you to go on lunch, etc. That's for salaried workers. I'm not saying don't go on lunch, I'm just saying you can't charge for that in good faith.

In a single day, you should target 5/6 hours of billable work. The extra 2-3 hours are for lunch, and other management type work you need to do to keep your freelance business afloat.

Btw, not to be a broken record, but you should try charging either by the day or by the project. It's just more security and takes the pressure off of needing to justify every individual hour spent.

Another tidbit of advice: use https://contractrates.fyi to figure out what you should be charging by the hour. A solid chance that you are undercharging.