In the SharePoint Admin center it is possible to set the default for link sharing of a site to "People with Existing Access".
For some sites, we would like to not only enable this setting as the default, but also hide the other options, so that "People with Existing Access" is the only way to share.
Is this possible?
Short answer: No.
It's one of those things where Microsoft have decided what's good for you. You can set the default to "People with Existing Access" and hope that people won't find the other options, but you can't hide them.
The approach here needs to be user training and making users understand that sharing is designed to give people access, not point them to a location of a file.
I feel that Microsoft has never really considered that people will be sending links to files to each other, because it's otherwise hard to locate a file. Again, something that can be solved with user training and better information architecture, theoretically, but in reality, many SharePoint sites have been modeled after the file shares they used to be, and files are still deeply hidden in folders, without any metadata that could help findability. So, sending a link to a file is often the quickest way to help someone locate it.
As mentioned, changing to only option is currently not supported. We can try to set the link as the default "people with existing access" through Powershell.
Set-SPOSite -identity https://YourTenant.sharepoint.com/sites/YourSite -DefaultLinkToExistingAccess 1
