[DOCS] Apply selected README and documentation fixes (#36535)

PR body:

  ### Details:
- Apply selected small documentation fixes from external documentation
PRs:
- PR #34505: fix malformed Markdown code fences and a duplicated
blockquote marker in `docs/documentation_build_instructions.md`.
     - PR #34551: fix two broken README documentation links:
       - Integrations link
       - GenAI detailed guide link
- PR #35009: add spacing between the OpenVINO Notebooks link and the
book emoji in `README.md`.
- PR #34981: add a simple README installation verification step, with
the Markdown fixed locally.
- Preserve the generic `<openvino_repository_url>` placeholder from
`docs/documentation_build_instructions.md` instead of applying PR
#34505's hard-coded upstream clone URL, because the placeholder is more
appropriate for forks, mirrors, and internal checkouts.
- Use PR #34551's direct OpenVINO Integrations page instead of duplicate
PR #35083's broader ecosystem page.
- Use PR #35009 as the applied source for the README spacing fix; PR
#35008 contains the same patch.
- Fix PR #34981's missing Python code fence before applying the
verification snippet.

  ### Validation:
- Ran Sphinx documentation build successfully after the
`docs/documentation_build_instructions.md` fix:
     - `cmake --build build --target sphinx_docs -j2`
     - Build completed with existing warnings.
   - Verified replacement README documentation URLs return HTTP 200.
   - Ran `git diff --check -- README.md`.
   - Validated the README verification snippet syntax.
- Confirmed `openvino.__version__` is used in existing OpenVINO
sources/docs.

  ### Tickets:
   - N/A
   - Related PRs: #34505, #34551, #35009, #34981
   - Related duplicate PRs: #35083, #35008

  ### AI Assistance:
   - AI assistance used: yes
- AI was used to inspect the existing backlog PRs, compare duplicate
patches, prepare local edits, and summarize validation results.
- Human validation included reviewing the selected changes, confirming
which original PR changes to preserve or omit, running local
   checks/builds, and deciding which PRs should be handled manually.

Author: michalzx

README.md

@@ -6,7 +6,7 @@ Open-source software toolkit for optimizing and deploying deep learning models.
 </h3>
 
 <p align="center">
- <a href="https://docs.openvino.ai/2026/index.html"><b>Documentation</b></a> • <a href="https://blog.openvino.ai"><b>Blog</b></a> • <a href="https://docs.openvino.ai/2026/about-openvino/key-features.html"><b>Key Features</b></a> • <a href="https://docs.openvino.ai/2026/get-started/learn-openvino.html"><b>Tutorials</b></a> • <a href="https://docs.openvino.ai/2026/documentation/openvino-ecosystem.html"><b>Integrations</b></a> • <a href="https://www.intel.com/content/www/us/en/developer/tools/openvino-toolkit/model-hub.html"><b>Benchmarks</b></a> • <a href="https://github.com/openvinotoolkit/openvino.genai"><b>Generative AI</b></a>
+ <a href="https://docs.openvino.ai/2026/index.html"><b>Documentation</b></a> • <a href="https://blog.openvino.ai"><b>Blog</b></a> • <a href="https://docs.openvino.ai/2026/about-openvino/key-features.html"><b>Key Features</b></a> • <a href="https://docs.openvino.ai/2026/get-started/learn-openvino.html"><b>Tutorials</b></a> • <a href="https://docs.openvino.ai/2026/about-openvino/openvino-ecosystem/openvino-integrations.html"><b>Integrations</b></a> • <a href="https://www.intel.com/content/www/us/en/developer/tools/openvino-toolkit/model-hub.html"><b>Benchmarks</b></a> • <a href="https://github.com/openvinotoolkit/openvino.genai"><b>Generative AI</b></a>
 </p>
 
 [![PyPI Status](https://badge.fury.io/py/openvino.svg)](https://badge.fury.io/py/openvino)
@@ -35,13 +35,22 @@ Check out the [OpenVINO Cheat Sheet](https://docs.openvino.ai/2026/_static/downl
 pip install -U openvino
 ```
 
+### Verify Installation
+
+After installation, you can verify OpenVINO is installed correctly by running:
+
+```python
+import openvino as ov
+print(ov.__version__)
+```
+
 Check [system requirements](https://docs.openvino.ai/2026/about-openvino/release-notes-openvino/system-requirements.html) and [supported devices](https://docs.openvino.ai/2026/documentation/compatibility-and-support/supported-devices.html) for detailed information.
 
 ## Tutorials and Examples
 
 [OpenVINO Quickstart example](https://docs.openvino.ai/2026/get-started.html) will walk you through the basics of deploying your first model.
 
-Learn how to optimize and deploy popular models with the [OpenVINO Notebooks](https://github.com/openvinotoolkit/openvino_notebooks)📚:
+Learn how to optimize and deploy popular models with the [OpenVINO Notebooks](https://github.com/openvinotoolkit/openvino_notebooks) 📚:
 - [Create an LLM-powered Chatbot using OpenVINO](https://github.com/openvinotoolkit/openvino_notebooks/blob/latest/notebooks/llm-chatbot/llm-chatbot-generate-api.ipynb)
 - [YOLOv11 Optimization](https://github.com/openvinotoolkit/openvino_notebooks/blob/latest/notebooks/yolov11-optimization/yolov11-object-detection.ipynb)
 - [Text-to-Image Generation](https://github.com/openvinotoolkit/openvino_notebooks/blob/latest/notebooks/text-to-image-genai/text-to-image-genai.ipynb)
@@ -100,7 +109,7 @@ OpenVINO supports the CPU, GPU, and NPU [devices](https://docs.openvino.ai/2026/
 
 ## Generative AI with OpenVINO
 
-Get started with the OpenVINO GenAI [installation](https://docs.openvino.ai/2026/get-started/install-openvino/install-openvino-genai.html) and refer to the [detailed guide](https://docs.openvino.ai/2026/openvino-workflow-generative/generative-inference.html) to explore the capabilities of Generative AI using OpenVINO.
+Get started with the OpenVINO GenAI [installation](https://docs.openvino.ai/2026/get-started/install-openvino/install-openvino-genai.html) and refer to the [detailed guide](https://docs.openvino.ai/2026/openvino-workflow-generative/inference-with-genai.html) to explore the capabilities of Generative AI using OpenVINO.
 
 Learn how to run LLMs and GenAI with [Samples](https://github.com/openvinotoolkit/openvino.genai/tree/master/samples) in the [OpenVINO™ GenAI repo](https://github.com/openvinotoolkit/openvino.genai). See GenAI in action with Jupyter notebooks: [LLM-powered Chatbot](https://github.com/openvinotoolkit/openvino_notebooks/tree/latest/notebooks/llm-chatbot) and [LLM Instruction-following pipeline](https://github.com/openvinotoolkit/openvino_notebooks/tree/latest/notebooks/llm-question-answering).
 

docs/documentation_build_instructions.md

@@ -27,11 +27,11 @@ $ source env/bin/activate
 5. Install the sphinx theme
 ```
 (env) $ python -m pip install docs/openvino_sphinx_theme
-``````
+```
 6. Install the custom sphinx sitemap
 ```
 (env) $ pip install docs/openvino_custom_sphinx_sitemap
-``````
+```
 7. Create build folder:
 ```
 (env) $ mkdir build && cd build
@@ -48,5 +48,5 @@ Depending on the needs, following variables can be added to first cmake call:
 - building Notebooks:  `-DENABLE_NOTEBOOKS=ON`
 - building OVMS:       `-DENABLE_OVMS=ON -DOVMS_DOCS_DIR=<path_to_OVMS_repo>`
 
-> > **Note:** When building the Python API documentation, the OpenVINO package version specified in [conf.py](./sphinx_setup/conf.py) is automatically downloaded using the [installation script](./scripts/install_appropriate_openvino_version.py).  
+> **Note:** When building the Python API documentation, the OpenVINO package version specified in [conf.py](./sphinx_setup/conf.py) is automatically downloaded using the [installation script](./scripts/install_appropriate_openvino_version.py).  
 > If you need a specific version or want to use an already installed OpenVINO package, modify these files accordingly.