My intention is to run python code 24/7 over several months to collect data through API calls and alert me if certain conditions are met.
How can I do that without keeping the code running on my laptop 24/7? Is there a way of doing it in "the cloud"?
Preferably free but would consider paying. Simplicity also a plus.
There is a plenty of free possibilities. You can use heroku servers. They have a strong documentation for python and is free (but of course with limit on megabytes and time usage). Heroku is also good because they have a lot of extensions (databases, dashboards, loggers etc.). In order to deploy your app on heroku you need to have some experience of working with git (but not that much, don't worry).
Another possibility could be Google Cloud Platform, which should be also easy to use.