You are experiencing a fairly normal event for a well with pump and pressure tank, though if the behavior seems new & different the pressure tank may require maintenance or repair/replacement.
Most well pumps (there are exceptions, such as "constant pressure pumps") run on a simple differential pressure switch with a 20 PSI differential (often non-adjustable) and a somewhat adjustable setting (20/40, 30/50, 40/60 are probably the most common settings.) When no water is being used, the system holds pressure due to a pressure tank; when water is used, the pump is activated when the pressure tank falls below the lower setpoint, and the pressure rises as the pump runs, until it shuts off at the higher setpoint - water has been added to the pressure tank, which again supplies water until the lower set point is reached.
If the air cell (most typical these days is a "bladder" or "diaphragm" type of tank where are and water are separated by a membrane) has inadequate pressure (possibly due to a leak) the amount of water stored in the pressure tank becomes smaller, and the pump operates more frequently - this is both more noticeable to you, and worse for the pump's life expectancy.
If you turn off your pump and drain the water from the tank, the air pressure should be roughly 2 PSI below the lower setpoint (18, 28 or 38 PSI for the typical setpoints listed above.) If you can pump it up to that value and have it stay, that may be all you need to do - if you find the pump operating more frequently in a short time (and drain the tank again and find the air pressure is lower again), or you can't pump it up at all, you may need a new pressure tank or a new bladder (I have personally found replaceable bladders to be non-ecoomical .vs. just replacing the tank - shop and see what you find.)
It is also possible that your tank is fine, but could be larger (or could be two, which is effectively larger.)
Or, you could convert to a constant pressure pump system - but those have always seemed excessively expensive to solve a "problem" that isn't really a problem with a properly designed and functioning pressure tank system - to me. That's an opinion and budget call.
We are getting spikes in water pressure, measured at the main feed to the house, starting yesterday when the outdoor sprinkler was shut and winterized. I have a backflow preventer that is tested annually.
Best Answer
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.