Modify the definitions of the fields, to enable logs for the fields when you change them. This is shown in the following code snippet:

class LibraryBookRent(models.Model):
    _name = 'library.book.rent'
    _inherit = ['mail.thread', 'mail.activity.mixin']

    book_id = fields.Many2one('library.book', 'Book', required=True)
    borrower_id = fields.Many2one('res.partner', 'Borrower', required=True)
    state = fields.Selection([('ongoing', 'Ongoing'), ('returned', 'Returned')],
                             'State', default='ongoing', required=True,
                             track_visibility='always')
    rent_date = fields.Date(default=fields.Date.today, track_visibility='onchange')
    return_date = fields.Date(track_visibility='onchange')

Update the my_library module to apply the changes. Create a new record in the library.book.rent model, make some changes in the fields, and then return the book. If you check the chatter, you will see the following logs:

Whenever you make changes to state, rent_date, or return_date, you will see a new log in the chatter. This will help you to see the full history of the record.