Can you help me identify what the problem is and how can I prevent this? Where is this request coming from?
The shortcode is only processed on the frontend. As far as the block editor is concerned the URL specified is [picsum] which is an unprocessed shortcode.
There is no simple fix to this, and making it work will require extensive and continuous modifications to the fundamentals of how the block editor works that will lead to problems. For example, you could filter the block and dynamically replace the attribute with an actual URL, but then the new URL would get saved not the shortcode. Additionally, each shortcode will need to be processed via an AJAX call and independently, so they would not interact with each other, breaking a lot of functionality based on shared variables. At any moment the core blocks behaviour may remove all of this, undoing all the work. Also what should happen if the user tries to edit the image, crop/rotate, or replace it? You can’t crop a shortcode.
Shortcodes in HTML attributes are not the solution you were hoping for and you have hit a dead end.
In this specific example, it would be easier to create an attachment that has an image URL generated by filters so that it’s the equivalent of the picsum shortcode, but this is a separate task and one that likely does not help you as you mention in the comments this is just a simplified example.
Fundamentally this will require either creating custom blocks or implementing alternatives using filters.
For example, if your goal is to dynamically populate the src for the image, you can use JS filters to add props and controls for choosing a data source, then replace core attributes with the dynamic values. You can the use the PHP block rendering filters to place the dynamic values in the src html attribute when the content is rendered.
For inline text, the rich-text format library API can be used to insert a shortcode while displaying the processed value to the user. This is very similar to how inline images work where an image block is inserted inline yet an inline image tag is what gets saved