Is it possible to increase the GraphQL API request timeout?

Yes, it is. The default is 15 seconds, but you can increase it up to 60 seconds using the configuration variable prefect.context.config.cloud.request_timeout.

Environment variable:

export PREFECT__CLOUD__REQUEST_TIMEOUT=60

config.toml:

[cloud]
request_timeout = 60

It works the same way for both Prefect Cloud and Prefect Server.

For more background on this, see the pull request: Increase Prefect Client HTTP Request Timeout by AndrewHannigan · Pull Request #4119 · PrefectHQ/prefect · GitHub

From a Slack discussion: