Song page behaviours

Some behaviours in the Songs page should be changed:

- After updating a song from the form and arriving at the song page, the back button in the browser should take you back to the search page. Currently, it takes you back to the form page. (This can be done by changing the `router.push` to a `router.back`.)
- After updating a song from the form and arriving at the song page, the song text (and author and melody) should be updated. Currently, it is not.

Start at the Songs page update flow and inspect the navigation used after submitting the form, including the router.push mentioned in the issue. Confirm that returning with the browser back button reaches the search page and that the song text, author, and melody shown on the song page reflect the update.

索引モデルが issue の本文から書いたものです。