Reminds me of the older versions of Opera browser, before they became another Chrome clone.
There was a “Links” sidebar, where which would list all the links on the page. You could then filter them, select a subset, and do some action - maybe open in a new tab or mass-download.
For the sharing use case described a nice option is WevDAV. macOS, Windows and many Linux file managers have support and for the read-only case it is basically an extra HTTP verb that provides a machine-readable directory listing.
Of course this doesn't solve the consumer side that is described here.
There was a “Links” sidebar, where which would list all the links on the page. You could then filter them, select a subset, and do some action - maybe open in a new tab or mass-download.