Fix broken links after flattening contribute folder

Author: leemthompo

contribute-docs/legacy-docs.md

@@ -38,7 +38,7 @@ For complex or multi-page updates to legacy documentation, refer to the [legacy
 If you need to merge changes that are published in both systems (usually because a change is valid in multiple product versions, such as stack 9.x and 8.x), it is recommended to update the documentation in elastic.co/docs first. Then you can convert the updates to ASCIIDoc and make the changes to the elastic.co/guide documentation. To do this, follow these steps:
 
 1. Install [pandoc](https://pandoc.org/installing.html) to convert your markdown file to ASCIIDoc
-2. Update the /docs content first in Markdown as described in [Contribute on the web](contribute/on-the-web.md) in the relevant repository.
+2. Update the /docs content first in Markdown as described in [Contribute on the web](on-the-web.md) in the relevant repository.
 3. Run your changes through pandoc:
    1. If you need to bring over the entire file, you can run the following command and it will create an ASCIIDoc file for you: `pandoc -f gfm -t asciidoc ./<file-name>.md -o <file-name>.asciidoc`
    2. If you just need to port a specific section you can use: `pandoc -f gfm -t asciidoc ./<file-name>.md` and the output of the file will be in your command window from which you can copy.

contribute-docs/syntax/_snippets/stack-serverless-lifecycle-example.md

@@ -8,7 +8,7 @@ applies_to:
 ---
 ```
 
-Because these changes need to be published as soon as the feature is released in Serverless, you might need to publish your docs before the feature is available in the {{stack}}. To allow for this, Docs V3 [displays badges differently](/contribute-docs/contribute/how-to/cumulative-docs/index.md#how-do-these-tags-behave-in-the-output) when the `applies_to` tag specifies a product version that has not yet been released to customers.
+Because these changes need to be published as soon as the feature is released in Serverless, you might need to publish your docs before the feature is available in the {{stack}}. To allow for this, Docs V3 [displays badges differently](/contribute-docs/how-to/cumulative-docs/index.md#how-do-these-tags-behave-in-the-output) when the `applies_to` tag specifies a product version that has not yet been released to customers.
 
 * A feature is tagged as available in a current Serverless release and a future {{stack}} version will render the following badges:
 

contribute-docs/syntax/quick-ref.md

@@ -391,7 +391,7 @@ Standard Markdown images: `[alt text]` in square brackets, followed by the image
 
 **DOs**<br>
 ✅ **Do:** Store images in a centralized directory<br>
-✅ **Do:** Follow v3 [best practices for screenshots](../contribute/how-to/cumulative-docs/badge-placement.md#images)<br>
+✅ **Do:** Follow v3 [best practices for screenshots](../how-to/cumulative-docs/badge-placement.md#images)<br>
 ✅ **Do:** Specify `:screenshot:` in an [image directive](images.md#screenshots) to add a border
 
 **DON'Ts**<br>