Migrate QA to SciMLTesting 2.4

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Summary

• migrate both test environments to SciMLTesting 2.4 and use the strict default QA runner
• remove undocumented SciMLBase blanket reexports and dependency-internal accesses
• document and test the public PSO algorithm extension interface
• use public SciMLBase.NonlinearProblem instead of the undocumented immutable problem type
• release as 1.2.0: this PR adds documented public APIs; no pre-existing documented API was removed

Validation

• PPS_TEST_GROUP=Everything Pkg.test() on Julia 1.12: regression (49), reinitialization, extension-interface (3), and CPU backend (26) tests passed; strict QA passed 20/21 checks
• the sole remaining QA failure is Atomix 1.1.3 not declaring its documented @atomic and @atomicreplace macros public; no QA exception was added
• julia -m Runic --check src test docs
• git diff --check