There is a short-term carry-over of fatigue from ST to the regular season for pitchers. But it's short-term only, not long-term and/or cumulative.
And for pitchers on the major league roster, that short-term effect is often negated by the fact that you have 4/5 cycles of off-days during the "Prepare for Regular Season" part of the schedule where recovery happens. Most ML pitchers start the season fully rested (unless they were abused during spring training by pitching at 0 (0), or if they have very low durability and by their nature recover slowly
The same is not true for minor leaguers, because they don't have any fatigue recovery from the end of ST to the beginning of the minor league season which, to me, is a flaw in the design of the engine.