I think this gets seen in black-and-white too often 🤔 It's neither pure moneymaking nor the miracle cure for high bills. It really just depends on how you want to use it and whether you're actually willing to change your habits.
We've had one of these meters at home for about half a year now, and honestly: just having the thing doesn't automatically lower your bill. Sure, it shows you how much water's flowing, but if you're not going to shower differently or stop lingering at the tap anyway, nothing changes. The real value is more that leak-detection thing other people mentioned - that's actually worth something. For me it quickly turned out that the toilet's constantly dripping a tiny bit (you can't even hear it normally), and that costs real money over the course of a year. Without the digital meter I probably never would've noticed 💧
As for you as a tenant: the important thing is how the billing works. If your landlord used to charge you a flat rate and now wants you to pay a share based on actual usage, you need to be careful - that could actually end up costing you more. Ask exactly how the billing will work before the meter gets installed. Otherwise: it doesn't cost you anything extra, and even if you don't consciously save water, at least you've got control and you'll notice right away if something's off.