Implement AbstractMCMC.{to,from}_samples (again)

[penelopeysm]

This is essentially the same PR as #1087, copy pasted but just with a different name (AbstractMCMC.to_samples instead of DynamicPPL.from_chains, and AbstractMCMC.from_samples instead of DynamicPPL.to_chains).

This follows on from TuringLang/AbstractMCMC.jl#184.

Since #1087 was already reviewed and discussed quite extensively, and this is completely the same code, I will probably merge this once CI passes.

[codecov]

Codecov Report

❌ Patch coverage is 96.15385% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.50%. Comparing base (ab6f38a) to head (6117826).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/chains.jl	92.59%	2 Missing ⚠️
ext/DynamicPPLMCMCChainsExt.jl	98.03%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1112      +/-   ##
==========================================
+ Coverage   81.23%   81.50%   +0.26%     
==========================================
  Files          40       40              
  Lines        3805     3844      +39     
==========================================
+ Hits         3091     3133      +42     
+ Misses        714      711       -3     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[github-actions]

Benchmark Report for Commit 6117826

Computer Information

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

Benchmark Results

┌───────────────────────┬───────┬─────────────┬───────────────────┬────────┬────────────────┬─────────────────┐
│                 Model │   Dim │  AD Backend │           VarInfo │ Linked │ t(eval)/t(ref) │ t(grad)/t(eval) │
├───────────────────────┼───────┼─────────────┼───────────────────┼────────┼────────────────┼─────────────────┤
│ Simple assume observe │     1 │ forwarddiff │             typed │  false │            6.4 │             1.9 │
│           Smorgasbord │   201 │ forwarddiff │             typed │  false │          744.9 │            42.1 │
│           Smorgasbord │   201 │ forwarddiff │ simple_namedtuple │   true │          432.1 │            54.0 │
│           Smorgasbord │   201 │ forwarddiff │           untyped │   true │          812.0 │            35.6 │
│           Smorgasbord │   201 │ forwarddiff │       simple_dict │   true │         6923.1 │            29.6 │
│           Smorgasbord │   201 │ forwarddiff │      typed_vector │   true │          772.9 │            40.7 │
│           Smorgasbord │   201 │ forwarddiff │    untyped_vector │   true │          818.4 │            35.4 │
│           Smorgasbord │   201 │ reversediff │             typed │   true │          943.7 │            44.7 │
│           Smorgasbord │   201 │    mooncake │             typed │   true │          756.3 │             5.8 │
│           Smorgasbord │   201 │      enzyme │             typed │   true │          945.9 │             3.7 │
│    Loop univariate 1k │  1000 │    mooncake │             typed │   true │         4009.9 │             5.9 │
│       Multivariate 1k │  1000 │    mooncake │             typed │   true │         1032.5 │             9.0 │
│   Loop univariate 10k │ 10000 │    mooncake │             typed │   true │        44158.8 │             5.3 │
│      Multivariate 10k │ 10000 │    mooncake │             typed │   true │         8716.6 │            10.3 │
│               Dynamic │    10 │    mooncake │             typed │   true │          126.2 │            12.1 │
│              Submodel │     1 │    mooncake │             typed │   true │            9.3 │             6.3 │
│                   LDA │    12 │ reversediff │             typed │   true │         1043.2 │             2.0 │
└───────────────────────┴───────┴─────────────┴───────────────────┴────────┴────────────────┴─────────────────┘

[github-actions]

DynamicPPL.jl documentation for PR #1112 is available at:
https://TuringLang.github.io/DynamicPPL.jl/previews/PR1112/