Apply manual edits to the how-to-contribute guide

Author: timmens

docs/source/development/how_to_contribute.md

@@ -37,7 +37,7 @@ contribution process (see Notes below).
 For regular contributors: **Clone** the [repository](https://github.com/optimagic-dev/optimagic/) to your local machine and create a new branch for implementing your changes. You can push your branch directly to the remote optimagic repository and open a PR from there.
 ```
 
-2. Clone your forked repository to your disk. This is where you'll make all your
+1. Clone your forked repository to your disk. This is where you'll make all your
    changes.
 
 1. Open your terminal and execute the following commands from the root directory of your
@@ -54,16 +54,17 @@ For regular contributors: **Clone** the [repository](https://github.com/optimagi
    installing it globally using pixi or uv.
    ```
 
-   To see all available pixi tasks, run:
+   You can then run the test suite with:
 
    ```console
-   $ pixi task list
+   $ pixi run tests
    ```
 
-   You can then run the test suite with:
+   which installs the development dependencies and runs pytest. To see all available
+   pixi tasks, run:
 
    ```console
-   $ pixi run tests
+   $ pixi task list
    ```
 
 1. Implement your fix or feature. Use git to add, commit, and push your changes to the
@@ -74,18 +75,14 @@ For regular contributors: **Clone** the [repository](https://github.com/optimagi
 1. Contributions are validated in two main ways. We run a comprehensive test suite to
    ensure compatibility with the existing codebase and employ
    [pre-commit hooks](https://effective-programming-practices.vercel.app/git/pre_commits/objectives_materials.html)
-   to maintain quality and adherence to our style guidelines. Opening a PR (see
-   paragraph 7 below) triggers optimagic's
+   to maintain quality and adherence to our style guidelines. Opening a PR (see below)
+   triggers optimagic's
    [Continuous Integration (CI)](https://docs.github.com/en/actions/automating-builds-and-tests/about-continuous-integration)
-   workflow, which runs the full `pytest` suite, pre-commit hooks, and other checks on a
+   workflow, which runs the full test suite, pre-commit hooks, and other checks on a
    remote server.
 
    You can also run the test suite locally for
-   [debugging](https://effective-programming-practices.vercel.app/debugging/pdbp/objectives_materials.html):
-
-   ```console
-   $ pytest
-   ```
+   [debugging](https://effective-programming-practices.vercel.app/debugging/pdbp/objectives_materials.html).
 
    With pre-commit installed, linters run before each commit. Commits are rejected if
    any checks fail. Note that some linters may automatically fix errors by modifying the
@@ -95,18 +92,16 @@ For regular contributors: **Clone** the [repository](https://github.com/optimagi
 Skip the next paragraph if you haven't worked on the documentation.
 ```
 
-6. Assuming you have updated the documentation, verify that it builds correctly. From
-   the root directory of your local optimagic repo, navigate to the docs folder and set
-   up the optimagic-docs environment:
+1. Assuming you have updated the documentation, verify that it builds correctly. Run:
 
    ```console
    $ pixi run build-docs
    ```
 
-   This command builds the HTML documentation, saving all files in the `build/html`
+   This command builds the HTML documentation, saving all files in the `docs/build/html`
    directory. You can view the documentation with your preferred web browser by opening
-   `build/html/index.html` or any other file. Similar to the online documentation, you
-   can navigate to different pages simply by clicking on the links.
+   `docs/build/html/index.html` or any other file. Similar to the online documentation,
+   you can navigate to different pages simply by clicking on the links.
 
 1. Once all tests and pre-commit hooks pass locally, push your changes to your forked
    repository and create a pull request through GitHub: Go to the Github repository of