Fix resume_from for parallel sampling

[penelopeysm]

Closes #1033

[penelopeysm]

Now if you call sample(..., MCMCThreads(), ...; resume_from=chn then initial_state will be correctly loaded before being sent to AbstractMCMC.

The only requirement for this to work is then that initial_state must be a vector containing exactly nchains final states. For MCMCChains this is not currently true, but it will be fixed by TuringLang/MCMCChains.jl#488, hence the need for that PR.

[github-actions]

Benchmark Report for Commit c84699d

Computer Information

Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 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 | Dimension |  AD Backend |      VarInfo Type | Linked | Eval Time / Ref Time | AD Time / Eval Time |
|-----------------------|-----------|-------------|-------------------|--------|----------------------|---------------------|
| Simple assume observe |         1 | forwarddiff |             typed |  false |                  8.9 |                 1.6 |
|           Smorgasbord |       201 | forwarddiff |             typed |  false |                664.9 |                42.0 |
|           Smorgasbord |       201 | forwarddiff | simple_namedtuple |   true |                438.1 |                53.6 |
|           Smorgasbord |       201 | forwarddiff |           untyped |   true |               1164.5 |                31.0 |
|           Smorgasbord |       201 | forwarddiff |       simple_dict |   true |               6809.4 |                28.0 |
|           Smorgasbord |       201 | reversediff |             typed |   true |               1067.4 |                41.2 |
|           Smorgasbord |       201 |    mooncake |             typed |   true |               1043.5 |                 4.5 |
|    Loop univariate 1k |      1000 |    mooncake |             typed |   true |               5932.7 |                 4.2 |
|       Multivariate 1k |      1000 |    mooncake |             typed |   true |               1007.9 |                 9.0 |
|   Loop univariate 10k |     10000 |    mooncake |             typed |   true |              67111.5 |                 3.8 |
|      Multivariate 10k |     10000 |    mooncake |             typed |   true |               8529.7 |                10.2 |
|               Dynamic |        10 |    mooncake |             typed |   true |                138.8 |                11.9 |
|              Submodel |         1 |    mooncake |             typed |   true |                 13.6 |                 4.9 |
|                   LDA |        12 | reversediff |             typed |   true |               1091.1 |                 6.8 |

[github-actions]

DynamicPPL.jl documentation for PR #1035 is available at:
https://TuringLang.github.io/DynamicPPL.jl/previews/PR1035/

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 82.34%. Comparing base (7f802f3) to head (c84699d).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1035      +/-   ##
==========================================
+ Coverage   82.26%   82.34%   +0.08%     
==========================================
  Files          38       38              
  Lines        3947     3949       +2     
==========================================
+ Hits         3247     3252       +5     
+ Misses        700      697       -3     

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[coveralls]

Pull Request Test Coverage Report for Build 17460622460

Details

• 2 of 2 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage decreased (-1.6%) to 80.966%

---

Totals
Change from base Build 17449211988:	-1.6%
Covered Lines:	3186
Relevant Lines:	3935

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 17460622460

Details

• 2 of 2 (100.0%) changed or added relevant lines in 1 file are covered.
• No unchanged relevant lines lost coverage.
• Overall coverage increased (+0.09%) to 82.601%

---

Totals
Change from base Build 17449211988:	0.09%
Covered Lines:	3252
Relevant Lines:	3937

---

💛 - Coveralls

[penelopeysm]

@joelkandiah I think this should make resume_from work as well, and I added the test you suggested -- could I trouble you to give it a try?