Replace PriorExtractorContext with PriorDistributionAccumulator

[mhauru]

I forgot about TuringLang/Turing.jl#2537 before implementing this, but I guess it's still a simple improvement even if soon it'll all be redone.

[github-actions]

Benchmark Report for Commit 2176a07

Computer Information

Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 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 |                  8.7 |                 1.6 |
|           Smorgasbord |       201 | forwarddiff |             typed |  false |                690.2 |                41.7 |
|           Smorgasbord |       201 | forwarddiff | simple_namedtuple |   true |                429.7 |                52.0 |
|           Smorgasbord |       201 | forwarddiff |           untyped |   true |               1248.3 |                28.5 |
|           Smorgasbord |       201 | forwarddiff |       simple_dict |   true |               8192.1 |                22.1 |
|           Smorgasbord |       201 | reversediff |             typed |   true |               1555.8 |                26.7 |
|           Smorgasbord |       201 |    mooncake |             typed |   true |               1015.8 |                 5.0 |
|    Loop univariate 1k |      1000 |    mooncake |             typed |   true |               5981.4 |                 3.9 |
|       Multivariate 1k |      1000 |    mooncake |             typed |   true |               1026.3 |                 8.8 |
|   Loop univariate 10k |     10000 |    mooncake |             typed |   true |              66825.6 |                 3.6 |
|      Multivariate 10k |     10000 |    mooncake |             typed |   true |               9261.5 |                 9.5 |
|               Dynamic |        10 |    mooncake |             typed |   true |                134.6 |                13.4 |
|              Submodel |         1 |    mooncake |             typed |   true |                 13.2 |                 6.2 |
|                   LDA |        12 | reversediff |             typed |   true |               1861.9 |                 2.4 |

[codecov]

Codecov Report

Attention: Patch coverage is 81.81818% with 4 lines in your changes missing coverage. Please review.

Please upload report for BASE (breaking@299e17b). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/extract_priors.jl	81.81%	4 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             breaking     #907   +/-   ##
===========================================
  Coverage            ?   84.52%           
===========================================
  Files               ?       37           
  Lines               ?     4052           
  Branches            ?        0           
===========================================
  Hits                ?     3425           
  Misses              ?      627           
  Partials            ?        0           

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