[codex] Fix density reinitialization callback

[svchb]

Summary

• store the particle system passed to DensityReinitializationCallback and reinitialize only that system
• trigger dt-based reinitialization when the requested interval is reached, not only after it is exceeded
• mark the integrator state as modified after density and pressure fields are changed
• add focused unit coverage for show output, dt triggering, and selected-system reinitialization

Root Cause

The callback constructor accepted a specific particle system, but the affect path called the global reinit_density!(vu_ode, semi) helper, which loops over every system in the semidiscretization. The time-based condition also used a strict > comparison, delaying callbacks that land exactly on the configured interval.

Validation

• julia --project=. -e 'using Test, TrixiParticles; include("test/callbacks/density_reinit.jl")'\n- julia --project=. -e 'using Test, TrixiParticles, Printf; include("test/callbacks/callbacks.jl")'

[codecov]

Codecov Report

❌ Patch coverage is 93.02326% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.91%. Comparing base (71d42df) to head (0f0e9a2).

Files with missing lines	Patch %	Lines
test/callbacks/density_reinit.jl	72.72%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1181      +/-   ##
==========================================
+ Coverage   89.88%   89.91%   +0.02%     
==========================================
  Files         133      134       +1     
  Lines       10452    10483      +31     
==========================================
+ Hits         9395     9426      +31     
  Misses       1057     1057              

Flag	Coverage Δ
total	89.91% <93.02%> (+0.02%)	⬆️
unit	70.90% <90.69%> (+0.41%)	⬆️

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[efaulhaber]

Doesn't work because the system might be replaced in the semidiscretization.