build(deps): Update NonlinearSolve requirement to 4.19.1 in /docs

[dependabot]

Updates the requirements on NonlinearSolve to permit the latest version.

Release notes

Sourced from NonlinearSolve's releases.

v4.19.1

NonlinearSolve v4.19.1

Diff since v4.19.0

Merged pull requests:

• Include reference to the latest 2026 improvements in MDPI Algorithms (#926) (@​Proektsoft-EOOD)
• Update to SciMLLogging 2.0 (#927) (@​jClugstor)
• Add ModAB algorithm to precompilation workload (#931) (@​Proektsoft-EOOD)

Closed issues:

• Cannot init(::NonlinearLeastSquaresProblem, NewtonRaphson()) with empty u0 (#912)

Commits

• 1010353 Update to SciMLLogging 2.0 (#927)
• d637062 Apply suggestion from @​ChrisRackauckas
• 1da0421 Limit algorithms to ModAB for bracketing solve
• e856faf Add ModAB algorithm to precompilation workload
• b15bf2b Update documentation with latest improvements
• 0ea19b8 Bump version from 4.18.0 to 4.19.0
• d72cd2d Bump Sundials and OrdinaryDiffEqTsit5 compat (consolidates #921–#924)
• 1e29383 Update Project.toml
• 560065e Avoid dense N×N Jacobian allocation for Anderson (#862)
• 45df1fe Bump julia-actions/setup-julia from 2 to 3
• Additional commits viewable in compare view

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[mmogib]

Closing in favor of CompatHelper (see #22) — Dependabot's julia ecosystem is being removed. docs/Project.toml carries no [compat] bounds, so the docs build always resolves current compatible versions; no pin needed.

[dependabot]

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