In Cursor, open Command Palette (Ctrl + Shift + P) and type Cursor: Attempt Update
However, in regard to the latter option, often the releases are rolled out, so you might see a new release in the changelog, but attempting to update via the Cursor interface will not work, because it is not available to your particular system yet.
I think it would be helpful if there was some visual feedback related to updating. In visual studio code, there is a gear-icon in the lower-left corner. When clicking on “check for update” a small badge icon appears near the gear indicating something is happening.
In cursor, Attempt to update is met with no visual feedback - nothing happens.