As halving progresses, it will get to a point where a single bitcoin will be mined for decades cause the mining reward has become so small, smaller than the transaction fees already. So 2140 or whenever the last sat is mined will not be an epoch for bitcoin, but a culmination of changes that has happened several years before that time.
Everyone validates transaction, and there is no actual puzzles being solved.
Nodes validate transactions.
- Jay -