[FEAT] Should include more comprehensive benchmarking (primarily performance)

Motivation

At present (b7dfe5cc), pybind11 proper only benchmarks compile-time and and artifact size for one given test setup (which tests arguments, simple inheritance, but that's about it, I think); the results of which can be seen here:
https://pybind11.readthedocs.io/en/stable/benchmark.html
https://github.com/pybind/pybind11/blob/v2.6.1/docs/benchmark.rst

However, it may difficult to objectively and concretely judge the performance impact of a PR, and weigh that against the value of the feature / issue resolution. Generally, benchmarking is done on an ad-hoc basis (totes works, but may make it difficult for less creative people like myself ;)

Primary motivating issues / PRs:

• https://github.com/pybind/pybind11/pull/2644#discussion_r549428425
• https://github.com/pybind/pybind11/issues/2646
• #1333

Secondary:

• #2322
• #1227 / #1825
• https://github.com/pybind/pybind11/pull/693#issuecomment-282592947
• #376

Fuzzy Scoping + Steps

1. Establish a baseline benchmarking setup that touches on the core "hotpath" features for performance. Only track metrics for a given version of pybind11 (out of scope: other binding approaches)

• Initialization time (e.g. dlopen - ish stuff, pybind11 internals upstart, binding registration, ...)
• Run time (function calls, type conversions, casting, etc.)
• Comparison "axes": later CPython versions, pybind11 versions / PR branches / forks
• OS: For now, just Linux ('cause that's all I use ;)

2. Add additional metrics (e.g. memory leaks / usage, do a redux on compile-time + size)
3. Ideally, provide guidance on what pybind11 finds the most important (how to weigh compile-time, size, speed, memory, etc.)
4. (Stretch) Possibly compare against other approaches (Boost.Python, Cython, SWIG, cppyy / Julia / LLVM-esque stuff, etc.)

Given that performance benchmarks can be a P.I.T.A. (e.g. how to OS + interrupts, hardware capacity / abstractions, blah blah), ideally decisions should be made about relative performance on the same machine. Ideally, we should also publish some metrics for a given config to give people a "feel" for the performance, as was done for compile time.

Suggested Solution Artifacts

• Identify code repository
  • Perhaps github.com/pybind/pybind-benchmarks ?
  • Alt.: In-tree (which may make it hard to compare across versions...)
• Identify good tooling for performance benchmarking
  • @henryiii suggested pytest-benchmark

@wjakob @rwgk @rhaschke @YannickJadoul @bstaletic @henryiii @ax3l
Can I ask what y'all think? Is this redundant w.r.t. what we already have?