Easiest way to get (dropbox) file datetime using a dropbox link

Using /2/sharing/get_shared_link_metadata is still the right way to get metadata from a shared link, and that now supports both User Authentication (using an access token, as before) as well as App Authentication (using an app key and secret instead of an access token). If that works better for your use case now, I suggest looking into that. You can get an app key and secret by registering an app here; be sure to use "Full Dropbox" access for this scenario (even though you won't need to actually connect it to an account and get an access token to call /2/sharing/get_shared_link_metadata with app authentication).

When calling /2/sharing/get_shared_link_metadata for a file, you can check the returned "rev" value, which is a revision identifier, in addition to "server_modified". Check out the documentation there for the full field information.

As for the etag value when accessing the shared link directly, that is still working and being returned with the etag for me when I try accessing a file directly using curl with a valid shared link to a file with "dl=1". I see in your output that you're getting back an HTML page. I recommend checking if the shared link you're using is still valid. You can manually try it in a web browser to see what that HTML page is; it may contain an error message regarding the shared link.

Also, the 'X-Dropbox-Request-Id' value is expected to change on every request, as that is an identifier for each request made to Dropbox, not the file being accessed itself.