Use Turing Actions for Documenter site and Navbar and upgrade package to use latest compats

[shravanngoswamii]

Until now docs were using old navbar injection script that breaks at many places. I have replaced it with Turing Actions and also updated docs workflow to use Turing Actions which supports adding navbar direectory.

I have also updated navbar design to support all Documenter themes and lets keep JuliaGP navbar in this org instead of Turing so I have added new it in .github repo: JuliaGaussianProcesses/.github#4

[codecov]

Codecov Report

❌ Patch coverage is 0% with 11 lines in your changes missing coverage. Please review.
✅ Project coverage is 0.00%. Comparing base (b962f5c) to head (030346a).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/LaplaceApproximationModule.jl	0.00%	11 Missing ⚠️

Additional details and impacted files

@@          Coverage Diff           @@
##           master    #151   +/-   ##
======================================
  Coverage    0.00%   0.00%           
======================================
  Files           5       5           
  Lines         325     325           
======================================
  Misses        325     325           

☔ 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.

[shravanngoswamii]

I have removed Julia 1.6 from tests and updraded few technicalities too. I think we can ignore Julia Nightly CI failure.

@yebai Can you have a look at them or can you please tag someone who maintains things here?

[github-actions]

ApproximateGPs.jl documentation for PR #151 is available at:
https://JuliaGaussianProcesses.github.io/ApproximateGPs.jl/previews/PR151/

[Copilot]

Pull request overview

This PR modernizes the documentation pipeline (Documenter v1 + TuringLang Actions + periodic navbar refresh) and updates parts of the code/tests/examples to be compatible with newer dependency APIs (notably Flux), alongside some internal refactors in the Laplace module.

Changes:

• Switch docs build/deploy and navbar injection to TuringLang GitHub Actions; update docs config for Documenter v1.
• Refactor Laplace cache internals to store diagonal terms as vectors and adjust related linear algebra / ChainRules.
• Update Flux usage in tests and examples (e.g., @layer, Adam, DataLoader) and broaden Flux compat in the test environment.

Reviewed changes

Copilot reviewed 14 out of 15 changed files in this pull request and generated 8 comments.

Show a summary per file

File	Description
docs/make.jl	Adjust example generation parallelism and Documenter HTML config.
docs/Project.toml	Bump Documenter compat to v1.
src/LaplaceApproximationModule.jl	Store W/Wsqrt as vectors; update Newton/Laplace computations and AD rules accordingly.
src/TestUtils.jl	Clarify test-stability comment about RNG differences across Julia releases.
examples/a-regression/script.jl	Update Flux APIs/macros used in the tutorial example.
test/runtests.jl	Add Logging to support logger silencing in tests.
test/LaplaceApproximationModule.jl	Add quiet_gradient helper and silence noisy Zygote logging in specific tests.
test/SparseVariationalApproximationModule.jl	Update ELBO assertion style; migrate Flux model to @layer and new training call shapes.
test/Project.toml	Add Logging and widen Flux compat range.
Project.toml	Broaden Julia compat from 1.6 to 1.
.github/workflows/CI.yml	Update CI matrix and action versions.
.github/workflows/Docs.yml	Replace docs steps with TuringLang/actions/DocsDocumenter.
.github/workflows/DocNav.yml	Replace custom navbar script with TuringLang/actions/DocsNav and scheduled rebuild.
.github/workflows/DocsPreviewCleanup.yml	Update checkout action version.
.github/workflows/Format.yml	Update checkout action version.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

You can also share your feedback on Copilot code review. Take the survey.

[shravanngoswamii]

@yebai I have addressed all Copilot suggestions!

[yebai]

Thanks @shravanngoswamii!