Hi Marijn,
Free tier only includes 1 GiB space. Based on your description that your app takes 1 GB and the error you are receiving when running touch, it would appear you have exceeded the quota limit of free plan.
In the Azure portal, please navigate to your web app, on left expand App Service plan, click Quotas. Once the Quota information displays on right, click File system usage. This will show you the disk usage for your plan. Sample screenshot:
I suggest scaling up to Basic B1, which includes 10 GiB space.
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP