Ignore until reviewed by @ChrisRackauckas.

Summary

• initialize only stored entries for constrained structured Jacobian/W prototypes instead of calling fill! on the logical matrix
• retain the existing sparse and dense initialization paths
• cover Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal, and UpperTriangular prototypes, including init/solve! coverage for diagonal and tridiagonal caches

Root cause

A clean-master bisect identified d8cbb9e4446427305484e25eb4c81c9f85c09277 (Initialize sparse Jacobian caches with stored values (#3833)) as the first bad commit. That change correctly avoided initializing sparse structural entries to zero, but routed every non-sparse prototype through fill!. fill!(::Diagonal, one(...)) attempts to write structural zeros outside the stored diagonal and throws.

The implementation uses public structured-array interfaces and the public backing storage of structured wrappers. SymTridiagonal requires a constructor/copyto! specialization because its public setindex! rejects off-diagonal writes even at stored positions.

Local verification

• focused include of default_linsolve_structure.jl on Julia 1.12.6: exit 0
• official GROUP=Downstream target testset: Default linsolve with structure | Pass 28 | Broken 2 | Total 30
• full Downstream process: exit 1 later in unrelated callback_detection.jl ordering assertions (lines 53 and 58); kept out of this branch for a separate clean-master investigation
• Runic on all four changed files: exit 0
• git diff --check: exit 0
• whole-repository Runic scan: the changed files pass; exit 1 only for unrelated existing DISCO formatting in lib/OrdinaryDiffEqCore/src/disco.jl, lib/OrdinaryDiffEqCore/src/integrators/controllers.jl, and test/Integrators_I/disco_tests.jl