There's really nothing all that mysterious. Chess engines are very sensitive to "horizon effect". Moving things forward a move or two where it can get a better glimpse of the future can profoundly affect its assessment. Take the one game I've played here. After 22...Nd6 the computer has me up just +1.5 pawns and will stay at that even if left to think a long time. However, move things forward four moves (down a forced line of exchanges) to move 26 and it takes just a few minutes for the eval starts to climb to +3.5 and beyond.
Understanding engine analysis

Download latest SF, let Stockfish run for approx 500 millions nodes per position u want to analyse.( That normally takes 1-2 minutes for 4 cores CPU , with single PV analysis).
You will hardly see such evaluation jump.(stable eval about 95% of the time)
Eval jump are due to Fail high or Fail low that usually occours in low depth.

Indeed. As with any engine analysis, brute force takes precedence over qualitative. "Quality" being in the eyes of the beholder and certainly beyond the realm of bytes n pieces. I think it's backwards to use engine analysis as your initial assessment of any given position. Even soo far as critique of a game. Only humans can understand the basic psychology of another human opponent. Although calculating concrete lines is, to me, it's ultimate strength. But weighing the potential values of each piece in a practical position where it's static or dynamic potential is abstract, you've got some grinding to do. Don't be lazy. Work it out yourself! Best wishes
Cc running stock fish Java engine very bad. Use fritz for analysis or manually do analysis with computer move by move. What should be hardware for computer for doing speedy analysis? What if I want to use Leela? Also use special modes in houfini very nice It will improve analysis if you don't have stamina for doing wait for hours.

Indeed. Heh with all this technical "engine" speak and lango, people say learning some critical lines in the Ponziani is only for 1600-1800+ players!? Oy very 8P

Download latest SF, let Stockfish run for approx 500 millions nodes per position u want to analyse.( That normally takes 1-2 minutes for 4 cores CPU , with single PV analysis).
You will hardly see such evaluation jump.(stable eval about 95% of the time)
Eval jump are due to Fail high or Fail low that usually occours in low depth.
This is precisely what the majority of official correspondence players are doing- and getting slaughtered.
For starters, single PV is acceptable only in simple positions. And 1-2 minutes is way less than enough, even in systems with 4x the cores you have mentioned...
1 hour analysis would be better than 1 min. But most peope here just do very low depth analysis ( OP used web engine SF9 with Multi PV =3, which is very slow and useless and can be used for blunder check only)
In 'auto analysis' the engine show "32.Rd2 Kg7 33.Kg2 and so" +2.85 that is ok. But when I play 32.Rd2 the engine show +1.85. three moves after 32.Rd2 +2.85 it is possible the engine show +0.85. I dont understand because 3 moves was in first analysis...
The CC engine is totally unstable...