Why does water pressure spike when sprinkler is winterized?

It seems you're saying the spikes become more noticeable during seasons when the sprinkler system is shut off/disconnected -- not when (while) the sprinkler system is being winterized. I think you have two questions: why do pressure spikes occur, and why does having the sprinkler system in service mitigate them?

Two common causes for water pressure spikes are water velocity and thermal expansion.

Water velocity

When a pipe is too small for the volume of water flowing through it the water has to flow very fast (distance per second) to meet the demand. Water has considerable mass; when the mass moves at high speed there's a lot of kinetic energy. When a valve closes while there's all this kinetic energy in the system you get water hammer, which manifests as a pressure spike and vibration of the pipes. A water hammer arrestor is a cushion, a shock absorber, which dissipates that energy in a safer (and quieter) way. It belongs near any valve which can close rapidly (a clothes or dish washer, usually).

Thermal expansion

Like many things, when water is heated it expands. Many people have a water heater with a tank; when the heated water is consumed and a new tank-load of cold water is heated the water expands. If this happens while all the system valves are closed the water is trapped inside the pipes and a rise in pressure occurs. This is especially problematic in metallic-piped systems (ie copper or steel plumbing). A water system should have a thermal expansion tank to absorb the expansion. Thermal expansion tanks require maintenance: ensure that the air bladder in the tank has no leaks and is pressurized with air correctly based on your water pressure.

You noted that pressure can be released by opening a valve but then pressure builds again a while later. The graph shows there may be some periodicity to it. This makes me lean toward a problem with the thermal expansion system, with pressure spikes corresponding to periodic re-heating of water in the heater tank.

What do sprinklers have to do with it

This is a big guessing game. You'll have to do experiments to prove or disprove any theories.

If high water velocity in the main line (upstream of your backflow preventer) is a problem, the plastic sprinkler pipes may stretch or otherwise provide a hammer-arresting effect during irrigation season.

If thermal expansion is a problem, maybe the backflow preventer has some minimal amount of leakage which allows the pressure to escape the house and dissipate by causing expansion of the plastic sprinkler pipes.