Cypress can't find server when checking out repo in Azure DevOps pipeline

A possible solution would be to check out both repositories in the same job like:

steps:
  - checkout: self
  - checkout: e2ecypress

The keyword self refers to the repository you execute the pipeline from, so your web app. But be aware that when checking out multiple repositories, the directory paths for them change a bit, see Docs: Check out multiple repositories in your pipeline

Then you can access the content from both repositories within the same job in a VM by using the correct paths. This allows you to do a build of your web app, launch it, and then run the Cypress tests on the running app.

To start your app, run the tests, and automatically exit the web app when finished, you can use the solution described in the following answer which is also recommend by Cypress: https://stackoverflow.com/a/70541458/6135684