如何快速筛选出部门下某用户未读的信件数？

有三张表
t_letter :表示信件表 （60万数据）索引如下：

t_letter_dep_map ：部门的信件的关联表 （30万数据）结构如下

索引如下：

t_read ：已读的数据表（150万数据）结构如下

索引如下：

我最开始写的SQL如下：

SELECT count(distinct `t_letter`.`id`)
FROM `t_letter`
    LEFT JOIN `t_letter_dep_map` `t_l_d_m` ON `t_l_d_m`.`depable_id` = `t_letter`.`id`
WHERE `t_letter`.`site_id` = 145
    AND `del_status` = 0
    AND (`letter_dep_id` = 206
        AND `depable_type` = 9)
    AND (`t_letter`.`id` NOT IN (
            SELECT `readable_id`
            FROM `t_read`
            WHERE `user_id` = 33203
                AND `cat` = 'all'
                AND `readable_type` = 9
        )
        AND `t_letter`.`time` > 1619402413)
    AND `t_letter`.`deleted_at` IS NULL

表示筛选出分配给部门id为206的并且用户id为33203在‘all’分类下还没有读的信件总数，这条sql耗时大概为10s。
explain 信息如下：

我参照网上的教程，讲sql改为left join之后情况也没有太大变化，耗时也是10秒左右

SELECT count(distinct `t_letter`.`id`)
FROM `t_letter`
    LEFT JOIN `t_letter_dep_map` `t_l_d_m` ON `t_l_d_m`.`depable_id` = `t_letter`.`id`
    LEFT JOIN (select * from `t_read` where `user_id` = 33203 and `cat` = 'all' and `readable_type` = 9) as `t_r` on `t_r`.`readable_id` = `t_letter`.`id`
WHERE `t_letter`.`site_id` = 145
    AND `del_status` = 0
    AND (`letter_dep_id` = 206
        AND `depable_type` = 9)
    AND 
        `t_r`.`readable_id` is null

        AND `t_letter`.`time` > 1619402413
    AND `t_letter`.`deleted_at` IS NULL

但是我在删除了部门的信件关联表之后，速度就变得很快，

SELECT count(distinct `t_letter`.`id`)
FROM `t_letter`
WHERE `t_letter`.`site_id` = 145
    AND `del_status` = 0
    AND (`t_letter`.`id` NOT IN (
            SELECT `readable_id`
            FROM `t_read`
            WHERE `user_id` = 33203
                AND `cat` = 'all'
                AND `readable_type` = 9
        )
        AND `t_letter`.`time` > 1619402413)
    AND `t_letter`.`deleted_at` IS NULL

只需要

这么短，那如何快速筛选出部门下某用户未读的信件数？