Add AirspeedVelocity benchmarking CI

.github/workflows/benchmark.yml

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+name: Benchmark this PR
+
+on:
+  pull_request:
+    branches: [master]
+    paths-ignore: ['docs/**']
+
+permissions:
+  pull-requests: write
+  contents: read
+
+jobs:
+  benchmark:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    strategy:
+      fail-fast: false
+      matrix:
+        version: ["1", "lts"]
+    env:
+      # Force consistent Julia depot path for self-hosted runners
+      JULIA_DEPOT_PATH: ~/.julia
+    steps:
+      - uses: MilesCranmer/AirspeedVelocity.jl@action-v1
+        with:
+          julia-version: ${{ matrix.version }}
+          script: "benchmark/benchmarks.jl"
+          extra-pkgs: ""
+          job-summary: true

benchmark/benchmarks.jl

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+using Pkg
+# Monorepo: the libraries live in lib/ — develop them so we benchmark this
+# checkout's code, not the registered versions.
+for lib in (
+        "ODEProblemLibrary", "DAEProblemLibrary", "DDEProblemLibrary",
+        "SDEProblemLibrary", "JumpProblemLibrary", "BVProblemLibrary",
+        "NonlinearProblemLibrary",
+    )
+    Pkg.develop(path = joinpath(@__DIR__, "..", "lib", lib))
+end
+
+using ODEProblemLibrary, DAEProblemLibrary, NonlinearProblemLibrary
+using BVProblemLibrary
+using BenchmarkTools
+
+const SUITE = BenchmarkGroup()
+
+# =============================================================================
+# Problem library loading (the package's job: constructing problems)
+# =============================================================================
+
+SUITE["ode"] = BenchmarkGroup()
+
+SUITE["ode"]["vanderpol"] = @benchmarkable ODEProblemLibrary.prob_ode_vanderpol
+SUITE["ode"]["lorenz"] = @benchmarkable ODEProblemLibrary.prob_ode_lorenz
+SUITE["ode"]["rober"] = @benchmarkable ODEProblemLibrary.prob_ode_rober
+SUITE["ode"]["brusselator_1d"] = @benchmarkable ODEProblemLibrary.prob_ode_brusselator_1d
+SUITE["ode"]["pleiades"] = @benchmarkable ODEProblemLibrary.prob_ode_pleiades
+SUITE["ode"]["hires"] = @benchmarkable ODEProblemLibrary.prob_ode_hires
+
+SUITE["dae"] = BenchmarkGroup()
+
+SUITE["dae"]["resrob"] = @benchmarkable DAEProblemLibrary.prob_dae_resrob
+
+SUITE["nonlinear"] = BenchmarkGroup()
+
+SUITE["nonlinear"]["testcase_lookup"] = @benchmarkable NonlinearProblemLibrary.nlprob_23_testcases["Generalized Rosenbrock function"]
+
+SUITE["bvp"] = BenchmarkGroup()
+
+SUITE["bvp"]["linear_1"] = @benchmarkable BVProblemLibrary.prob_bvp_linear_1