AIUI there's not really anything to miniaturise beyond the rest of the pacemaker (i.e. ignoring how it's powered) - there's no 'control' or addition of material as in a big nuclear power station, it's 'just' a decaying radioactive material -> heat -> electricity (the inverse of Peltier effect heating, and presumably just as inefficient (~30%?)).
You need a heat difference, not just heat, to generate electricity.
Now my sibling comment links to a paper where they say they can find heat differences in the body that are sufficient for their needs, so this is still a possibility! But it does mean you need to be somewhere with a heat gradient: the paper mentions just under the skin.
There are different kinds of nuclear power, and these types of small power-trickle devices have been around for decades. (Mostly in spacecraft, I think?)
Yup. All the US mars rovers use radioisotope generators that generate electricity by using the decay heat.
But some satellites actually had real fission reactors on board. The US had the experimental SNAP-10A satellite and the soviets used a small fission reactor in their RORSAT satellites to power a radar so they can detect NATO naval fleets.