Hi @Julien G
I'm glad to hear you solve the problem ,if you have any issue about SharePoint, you are welcome to raise a ticket in this forum.
By the way, since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others." and according to the scenario introduced here: Answering your own questions on Microsoft Q&A, I would make a brief summary of this thread:
[files deleted from Sharepoint in my local recycle bin]
Issue Symptom:
When someone deletes a file from Sharepoint on another computer, the deleted files end up directly in the computer's recycle bin.
Current status:
The basic operation of the OneDrive sync application is to download files locally that are tuned on the PC.
The "Files on Demand" feature has been implemented to help save space on the PC.
This allows you to access your online storage space in OneDrive without having to download everything and use the file storage space on your Windows device.
Online-only Files do not take up space on the computer. The file does not download to the device until you open it.
When you open an Online Only file, it is downloaded to your device and becomes a locally available file.
There is no automatic way to block files from downloading.
You can change the file to be available online only. Simply right-click on the file and select "Free Space". This is an action you must take on every file.
New files or folders created online or on another device are set as online only to save as much space as possible.
In order to automate the <Free Space> process a bit you can set the Windows Storage Assistant to automatically mark files as online only. For more details please see the following article: https://support.microsoft.com/fr-fr/office/utiliser-onedrive-et-l-assistant-stockage-dans-windows-10-pour-g%C3%A9rer-l-espace-disque-de5faa9a-6108-4be1-87a6-d90688d08a48
Also, you can find all the details about the "Files on Demand" feature in the article below:
You could click the "Accept Answer" button for this summary to close this thread, and this can make it easier for other community member's to see the useful information when reading this thread. Thanks for your understanding!