Issue #477: Add analytical likelihoods to R functionality

[seabbs]

Description

This PR closes #477. It also closes #538 and #526. It is a draft and so not suitable for review/merging.

This PR:

• Fixes a vector length issue for cens that was causing an issue for some likelihood calls
• Adds stan side support for fitting all distributions that primarycensored supports
• Adds support for R side analytical likelihoods (so far for just lognormal and gamma). Note this support has to be added here manually as new analytical solutions are added to primarycensored. This is unfortunate but I can't find a workaround.

I have checked the support for priorsense and loo. Without the analytical likelihoods the code in this PR enables these functions to run but with 10 cores loo still takes 5 minutes and priorsense runs for longer than I wanted to wait and see. With the analytical solutions enabled (this also side steps #476 hence the big speed up) loo takes a few seconds and priorsense takes less than 30 seconds for me (the code in the FAQ vignette).

Work to do:

• Add support for Weibull analytical solutions
• see if can reduce code duplication
• docs sweep
• fill testing gaps (including priorsense and loo)
• Add integration tests
• Turn on the eval false FAQ code
• linting

Checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have included the target issue or issues in the PR title in the for Issue(s) issue-numbers: PR title
• I have read the contribution guidelines.
• I have tested my changes locally.
• I have added or updated unit tests where necessary.
• I have updated the documentation if required.
• My code follows the established coding standards.
• I have added a news item linked to this PR.
• I have reviewed CI checks for this PR and addressed them as far as I am able.

[seabbs]

see if can reduce code duplication

Saving this to address with a more well-formed solution in #476.

[seabbs]

Another quite big PR with some masking linting and formatting fixes but all looks good to me and test coverage of the changes is highly.

Going to resolve the pre-commit issues which are due to Air and styler having a conflict in its own PR.

[codecov]

Codecov Report

Attention: Patch coverage is 98.81306% with 4 lines in your changes missing coverage. Please review.

Project coverage is 95.59%. Comparing base (f5eead1) to head (453e2b9).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
R/formula.R	0.00%	2 Missing ⚠️
R/simulate.R	75.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #540      +/-   ##
==========================================
+ Coverage   94.38%   95.59%   +1.20%     
==========================================
  Files          17       17              
  Lines         837      998     +161     
==========================================
+ Hits          790      954     +164     
+ Misses         47       44       -3     

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