Reading log counts in sidebar do not update when a book's status changes

After updating the status of a book in the reading log view, the log counts in the sidebar do not change.

### Evidence / Screenshot (if possible)
*Count is "1" after removing the only book from the "Currently Reading" log*
### Relevant url?

https://openlibrary.org/account/books

### Steps to Reproduce

1. Navigate to your reading log page. View any log that contains books.
2. Change the status of a book using the status drop-down input.
3. Note that the counts in the sidebar did not change.

* Actual: Counts in the sidebar do not change.
* Expected: Count in the sidebar accurately reflect the state of the patron's reading logs.

### Details

- **Logged in (Y/N)?** Y
- **Browser type/version?** N/A
- **Operating system?** N/A
- **Environment (prod/dev/local)?** prod

### Proposal & Constraints
- Avoid using jQuery.
- Identify other instances of this issue.
- Fix

### Related files

### Stakeholders