They last for a log time, but the important detail is that they have very low power, like 1mW with the size factor of a normal battery, so you need like a dozen for a (old) wrist watch and s few hundred to turn on a led.
More details in:
http://nanoscale.blogspot.com/2020/08/diamond-batteries-unli...
It seems like Carbon-14 is just not very radioactive, and if I read the Wikipedia article right, Geiger counters can't even detect the radiation for small amounts, which makes me wonder if they would even trigger around the 1 gram in those batteries.
Looking at a bit more sources, Carbon-14 radiation has a maximum distance of 22 cm in air and 0.27 mm in body tissue. The half-distance layer in water is 0.05 mm. In addition, Carbon-14 in nuclear waste tend to also include tritium, which is even weaker.
If we wanted powerful batteries, low-level waste seems like a bad choice. If the material don't even need shielding to be around, it is unlikely to carry a lot of energy. Intermediate-level waste and high-level waste would likely be better suited, especially Intermediate-level waste since those do carry a lot of energy but does not require cooling.
Of course, if you are using the nuclear stuff, you will prefer something shorter lived, so you can use a smaller battery. But I don't see why that huge objection on using the longer lived stuff too.