Welcome! Sounds like you're looking for a deployment step, please check out the following resources that should lead you to some useful information:
Specifically for setting up deployments:
For deploying with/to Google App Engine (GAE), you either need the GAE SDK image or more specialized in Bitbucket Pipelines you can make use of the GAE deployment pipe:
The pipe image is based on the official GAE Docker image which is providing the "gcloud" utility, my recommendation is to have the Pipeline similar to what you can do locally and therefore I would suggest to start with the offical GAE Docker image.
Put the command to deploy into the pipeline step script, use the GAE image in that step, setup the deployment and bind it to that step (see Step 2: Configure your deployment steps in Set up Bitbucket Deployments)
Testing your Pipeline
Testing a Pipeline is outlined in Debug pipelines locally with Docker (Atlassian Support Bitbucket Resources).
For running, testing and debugging Bitbucket Pipelines, I can also recommend a local pipelines runner named pipelines, e.g. as you might have PHP and you may already have Docker installed locally:
(full disclosure: I'm the author of that utility) Caveat: Throwing more tools onto your problem might not lead you to better answers per-se. E.g. if you don't have Docker installed locally yet, install it and start with the directions of Debug pipelines locally with Docker first to better understand how Bitbucket Pipelines work and how to do things in detail locally.
The pipelines utility adds some more options like validation and verification (e.g. dry-run) as well as running Bitbucket Pipelines locally similar to remote with a limited feature set, behind the scenes it just runs the step scripts in Docker containers defined in the bitbucket-pipelines.yml file. The benefit of it are faster iterations on bitbucket-pipelines.yml changes and getting the base setup to work. It does not have support for Pipes (yet), so there are some limitations, just saying.
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