Complete mixed kernel-gradient correction

[svchb]

Summary

• compose kernel and matrix correction caches with matching element types
• assemble the mixed matrix from the kernel-corrected raw gradient
• document constant and affine consistency
• add direct-gradient, restart, EDAC, boundary, and GPU tests

Stack

Depends on #1290. This PR targets main and temporarily includes the preceding stack.

Review-only diff: svchb/TrixiParticles.jlOpen@fix/gradient-correction-lifecycle...fix/mixed-kernel-gradient-correction

Isolated layer: 5 files, 63 additions, 3 deletions.

Verification

• complete unit suite passed
• JuliaFormatter and git diff --check passed

[codecov]

Codecov Report

❌ Patch coverage is 88.01170% with 41 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.49%. Comparing base (a720b1d) to head (fe0a364).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
test/examples/gpu.jl	0.00%	23 Missing ⚠️
src/schemes/structure/rigid_body/system.jl	46.15%	7 Missing ⚠️
...c/schemes/structure/total_lagrangian_sph/system.jl	57.14%	6 Missing ⚠️
src/general/corrections.jl	85.71%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1288      +/-   ##
==========================================
+ Coverage   90.39%   90.49%   +0.10%     
==========================================
  Files         138      144       +6     
  Lines       11322    11633     +311     
==========================================
+ Hits        10234    10527     +293     
- Misses       1088     1106      +18     

Flag	Coverage Δ
total	90.50% <88.01%> (+0.10%)	⬆️
unit	78.86% <85.38%> (+1.37%)	⬆️

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