ci: add workflow to build and publish docs

Add a workflow that, for now, builds Doxygen docs and published them on
Github pages.

Signed-off-by: Gerard Marull-Paretas <gerard@teslabs.com>

.github/workflows/docs.yml

@@ -0,0 +1,61 @@
+# Copyright (c) 2024, Nordic Semiconductor ASA
+# SPDX-License-Identifier: Apache-2.0
+
+name: Documentation
+
+on: [push, pull_request]
+
+env:
+  DOXYGEN_VERSION: 1.9.6
+
+jobs:
+  build:
+    runs-on: ubuntu-22.04
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Install dependencies
+        run: |
+          wget --no-verbose "https://github.com/doxygen/doxygen/releases/download/Release_${DOXYGEN_VERSION//./_}/doxygen-${DOXYGEN_VERSION}.linux.bin.tar.gz"
+          tar xf doxygen-${DOXYGEN_VERSION}.linux.bin.tar.gz
+          echo "${PWD}/doxygen-${DOXYGEN_VERSION}/bin" >> $GITHUB_PATH
+          pip install -r doc/requirements.txt
+
+      - name: Build
+        run: |
+          cd doc
+          doxygen
+
+          SPHINXOPTS="-W" make html
+
+          mkdir deploy
+          mv _build_doxygen/html deploy/doxygen
+          mv _build_sphinx/html deploy/sphinx
+
+      - name: Setup pages
+        if: github.event_name != 'pull_request'
+        uses: actions/configure-pages@v4
+
+      - name: Upload pages artifact
+        if: github.event_name != 'pull_request'
+        uses: actions/upload-pages-artifact@v3
+        with:
+          path: doc/deploy
+
+      - name: Upload artifacts
+        if: github.event_name == 'pull_request'
+        uses: actions/upload-artifact@v4
+        with:
+          path: doc/deploy
+
+  deploy:
+    runs-on: ubuntu-22.04
+    needs: build
+    if: github.event_name != 'pull_request'
+    permissions:
+      pages: write
+      id-token: write
+    steps:
+      - name: Deploy to GitHub Pages
+        uses: actions/deploy-pages@v4

README.md

@@ -1,4 +1,11 @@
 # Zephyr Example Application
+
+<a href="https://zephyrproject-rtos.github.io/example-application/doxygen">
+  <img alt="API Documentation" src="https://img.shields.io/badge/API-documentation-3D578C?logo=c&logoColor=white">
+</a>
+<a href="https://zephyrproject-rtos.github.io/example-application/sphinx">
+  <img alt="Documentation" src="https://img.shields.io/badge/documentation-3D578C?logo=sphinx&logoColor=white">
+</a>
 
 This repository contains a Zephyr example application. The main purpose of this
 repository is to serve as a reference on how to structure Zephyr-based