"My understanding is that particles arise as a computational tool."

This is a "cart before the horse" statement. Experiments determined that particles existed, then "computational tools" were found by mathematically wise physisists that could model the interactions of the observed particles.

Quantum fields are analogous to a coordinate system on which with differential operators on the named fields ( electron, neutrino...) one can mathematically model the real world existence and interactions of particles and check the validity of the model by comparing to data.

"My understanding is that particles arise as a computational tool."

This is a "cart before the horse" statement. Experiments determined that particles existed,( see here a bubble chamber photo of particle tracks) then "computational tools" were found by mathematically wise physisists that could model the interactions of the observed particles.

Quantum fields are analogous to a coordinate system on which with differential operators on the named fields ( electron, neutrino...) one can mathematically model the real world existence and interactions of particles and check the validity of the model by comparing to data.