This page looks like a good suumary of biblical punishments.
Fines and 'scourging' were indeed applied for some minor offences, but the death penalty applied much more commonly than seems reasonable to us today! It was a very different world.
The story of the man stoned for picking upsticks on the sabbath is - IMO - not a historical event but serves to illustrate the importance of observing the sabbath, as a symbol of observing the rules of the YHWHist religion generally. The priests could use the story as the precedent for harsh treatment of any Hewbrew or Jew who deviated from what was laid down. Thus the priests could maintain control and discipline over the exiles, hence ensuring that Jewish identity (or rather the yhwhists' prefered version of jewish identity) was preserved.
Rather like Islam today, there was no distnction made between national/ethnic identity and religious identity; in other words no distinction between treason and blasphemy. Ergo, a sabbath breaker was a traitor, and even in today's world often treason is a capital offence where murder is not.
