Restructure API reference and align docs checks with public API (#1620)

* Initial plan

* Restructure API reference documentation

Co-Authored-By: Claude Code (claude-sonnet-4-6) <noreply@anthropic.com>

* Adjust Documenter missing-docs check

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: Claude Code (claude-sonnet-4-6) <noreply@anthropic.com>

Author: Copilot

docs/make.jl

@@ -26,6 +26,7 @@ const contributing = [
 
 makedocs(;
     modules = [TulipaEnergyModel],
+    checkdocs = :exports,
     authors = "Abel Soares Siqueira <abel.s.siqueira@gmail.com>,Diego A. Tejada-Arango <diego.tejadaarango@tno.nl>,Germán Morales-España <german.morales@tno.nl>,Grigory Neustroev <G.Neustroev@tudelft.nl>,Juha Kiviluoma <Juha.Kiviluoma@vtt.fi>,Lauren Clisby <lauren.clisby@tno.nl>,Maaike Elgersma <m.b.elgersma@tudelft.nl>,Ni Wang <ni.wang@tno.nl>,Suvayu Ali <s.ali@esciencecenter.nl>,Zhi Gao <z.gao1@uu.nl>",
     sitename = "TulipaEnergyModel.jl",
     format = Documenter.HTML(; canonical = "https://TulipaEnergy.github.io/TulipaEnergyModel.jl"),

docs/src/70-reference.md

@@ -4,6 +4,17 @@
 Pages = ["70-reference.md"]
 ```
 
+## Public API
+
+The functions and types below form the supported public interface of
+TulipaEnergyModel.jl.
+
 ```@autodocs
 Modules = [TulipaEnergyModel]
+Private = false
 ```
+
+## Internal implementation details
+
+Internal helper functions (such as names starting with `_`) are not part of
+the public API and are intentionally omitted from this page.