Release prep: bump ModelingToolkitBase to 1.51.1

[ChrisRackauckas]

Registered 1.51.0 (homotopy operator/HomotopyProblem feature) unaffected. Releases the additional patch-level content since then: DiffEqBase 7.x compat floor raise (#4709) plus QA/docstring scaffolding. Root ModelingToolkit is already correctly at 11.31.2 in source (clean patch bump from registered 11.31.1) and needs no edit here, just a registration trigger after this merges.

[github-actions]

Benchmark Results (Julia vlts)

Time benchmarks

	master	683335f...	master / 683335f...
ODEProblem	4.99 ± 0.34 ms	5.03 ± 0.36 ms	0.993 ± 0.098
init	0.0565 ± 0.016 ms	0.0558 ± 0.014 ms	1.01 ± 0.39
large_parameter_init/ODEProblem	19.6 ± 2 ms	19.5 ± 2.4 ms	1 ± 0.16
large_parameter_init/init	0.0798 ± 0.028 ms	0.0742 ± 0.02 ms	1.08 ± 0.48
mtkcompile	7.71 ± 0.43 ms	7.86 ± 0.56 ms	0.98 ± 0.089
sparse_analytical_jacobian/ODEProblem	20 ± 1.2 ms	20.3 ± 1.2 ms	0.986 ± 0.083
sparse_analytical_jacobian/f_iip	0.063 ± 0.001 μs	0.061 ± 0.001 μs	1.03 ± 0.024
sparse_analytical_jacobian/f_oop	0.334 ± 0.013 ms	0.332 ± 0.015 ms	1.01 ± 0.062
time_to_load	5.2 ± 0.075 s	5.07 ± 0.17 s	1.02 ± 0.038

Memory benchmarks

	master	683335f...	master / 683335f...
ODEProblem	0.0395 M allocs: 1.99 MB	0.0395 M allocs: 2.01 MB	0.992
init	0.416 k allocs: 0.0697 MB	0.416 k allocs: 0.0697 MB	1
large_parameter_init/ODEProblem	0.323 M allocs: 11.3 MB	0.323 M allocs: 11.3 MB	1
large_parameter_init/init	0.604 k allocs: 0.172 MB	0.604 k allocs: 0.172 MB	1
mtkcompile	0.061 M allocs: 3.32 MB	0.061 M allocs: 3.32 MB	1
sparse_analytical_jacobian/ODEProblem	0.19 M allocs: 7.81 MB	0.19 M allocs: 7.81 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.634 k allocs: 19.6 kB	0.634 k allocs: 19.6 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[github-actions]

Benchmark Results (Julia v1)

Time benchmarks

	master	683335f...	master / 683335f...
ODEProblem	6.03 ± 0.47 ms	5.13 ± 0.45 ms	1.18 ± 0.14
init	0.0673 ± 0.02 ms	0.066 ± 0.019 ms	1.02 ± 0.42
large_parameter_init/ODEProblem	27.2 ± 3.7 ms	25.8 ± 5 ms	1.05 ± 0.25
large_parameter_init/init	0.0762 ± 0.038 ms	0.111 ± 0.049 ms	0.689 ± 0.46
mtkcompile	8.77 ± 0.38 ms	8.27 ± 0.61 ms	1.06 ± 0.09
sparse_analytical_jacobian/ODEProblem	24.4 ± 2.7 ms	22.9 ± 3.1 ms	1.07 ± 0.19
sparse_analytical_jacobian/f_iip	0.09 ± 0.001 μs	0.081 ± 0.01 μs	1.11 ± 0.14
sparse_analytical_jacobian/f_oop	0.126 ± 0.012 ms	0.119 ± 0.012 ms	1.06 ± 0.15
time_to_load	5.72 ± 0.097 s	5.7 ± 0.36 s	1 ± 0.065

Memory benchmarks

	master	683335f...	master / 683335f...
ODEProblem	0.0397 M allocs: 1.83 MB	0.0397 M allocs: 1.81 MB	1.01
init	0.415 k allocs: 0.0517 MB	0.415 k allocs: 0.0517 MB	1
large_parameter_init/ODEProblem	0.351 M allocs: 12.8 MB	0.35 M allocs: 12.7 MB	1.01
large_parameter_init/init	0.798 k allocs: 0.151 MB	0.798 k allocs: 0.151 MB	1
mtkcompile	0.0592 M allocs: 2.64 MB	0.0592 M allocs: 2.62 MB	1.01
sparse_analytical_jacobian/ODEProblem	0.185 M allocs: 6.88 MB	0.185 M allocs: 6.88 MB	1
sparse_analytical_jacobian/f_iip	0 allocs: 0 B	0 allocs: 0 B
sparse_analytical_jacobian/f_oop	0.848 k allocs: 27 kB	0.848 k allocs: 27 kB	1
time_to_load	0.145 k allocs: 11 kB	0.145 k allocs: 11 kB	1