There is a long, thin, rubber-y line wrapped around/connected to the water line pictured below.
Other angle:
The piece in question is loosely hanging via a zip tie on my main water line about shoulder height and can be moved up/down easily.
Yes, you get billed for water just like electricity and gas. Depending where you live it could be a bill every 3-6 months, or monthly. The western US is has a lot of desert and water is much more expensive than in wetter areas. Their bills are typically higher and more heavily tracked. If you have a leak you wouldn’t know for a couple months, having that happen in a water scarce area would be less than ideal for a customer.