You may try the following.

A LEFT JOIN was used to determine overlapping duration before aggregating the results to subtract the total overlapping duration from the actual task duration.

SELECT
     emp_id,
     task_id,
     MAX(task_duration) - SUM(overlap_duration/2) as hours
FROM (
    SELECT
        t1.emp_id,
        t1.task_id,
        t1.time_in,
        t1.time_out,
        (datediff(seconds, t1.time_in, t1.time_out)/3600) as task_duration,
         CASE
             WHEN t2.task_id IS NULL THEN 0
             ELSE (datediff(seconds,t2.time_in,t2.time_out)/3600)
         END as overlap_duration,
         t2.task_id as overlap_task
    FROM
        task_times t1
    LEFT JOIN
        task_times t2 ON t1.emp_id = t2.emp_id AND
                         t1.task_id < t2.task_id AND
                         (
                      (t1.time_in between t2.time_in and t2.time_out) or
  (t1.time_out between t2.time_in and t2.time_out) or
  (t1.time_in < t2.time_in and t1.time_out > t2.time_out) or
  (t1.time_in > t2.time_in and t1.time_out < t2.time_out)
                      )
                      
) t3
GROUP BY
    emp_id, task_id;

View working demo on DB Fiddle

I've also included the output of the subquery below for your perusal

SELECT
        t1.emp_id,
        t1.task_id,
        t1.time_in,
        t1.time_out,
        (datediff(seconds, t1.time_in, t1.time_out)/3600) as task_duration,
         CASE
             WHEN t2.task_id IS NULL THEN 0
             ELSE (datediff(seconds,t2.time_in,t2.time_out)/3600)
         END as overlap_duration,
         t2.task_id as overlap_task
    FROM
        task_times t1
    LEFT JOIN
        task_times t2 ON t1.emp_id = t2.emp_id AND
                         t1.task_id < t2.task_id AND
                         (
                      (t1.time_in between t2.time_in and t2.time_out) or
  (t1.time_out between t2.time_in and t2.time_out) or
  (t1.time_in < t2.time_in and t1.time_out > t2.time_out) or
  (t1.time_in > t2.time_in and t1.time_out < t2.time_out)
                      );

View demo on DB Fiddle

Edit 1

Responding to question update

Additional details:

1. The # of tasks that can overlap is variable, it's not only up to 2.
2. Employees may clock into the same task multiple times throughout the day

I've added more sample data and provided an updated fiddle. I'm unable to provide a demo fiddle with snowflake but we can change the EXTRACT to DATEDIFF as shown earlier.

CREATE TABLE task_times (
  emp_id INTEGER,
  task_id INTEGER,
  time_in TIMESTAMP,
  time_out TIMESTAMP
);

INSERT INTO task_times
  (emp_id, task_id, time_in, time_out)
VALUES
-- add repetition of the same tasks with overlaps
  ('43', '159221', '2021-09-30 09:00:00', '2021-09-30 14:30:00'),
  ('43', '159221', '2021-09-30 09:03:00', '2021-09-30 14:27:00'),
  ('43', '159221', '2021-09-30 09:03:00', '2021-09-30 14:38:00'),
--- add overlap of different tasks
  ('43', '188239', '2021-09-30 09:16:03', '2021-09-30 10:44:51'),
  ('43', '188239', '2021-09-30 09:16:03', '2021-09-30 10:43:51'),
  ('43', '177741', '2021-09-30 13:12:49', '2021-09-30 14:14:32'),
-- add multiple overalapping tasks with a difference of 10 minutes
  ('43', '333333', '2021-10-30 09:00:00', '2021-10-30 12:40:00'),
  ('43', '333334', '2021-10-30 09:00:00', '2021-10-30 12:30:00'),
  ('43', '333335', '2021-10-30 09:00:00', '2021-10-30 12:20:00'),
  ('43', '333336', '2021-10-30 09:00:00', '2021-10-30 12:10:00'),
-- add multiple log in and log out times with no overlaps
  ('43', '333337', '2021-10-30 09:00:00', '2021-10-30 12:00:00'),
  ('43', '333337', '2021-10-30 12:30:00', '2021-10-30 13:00:00'),
  ('43', '333337', '2021-10-30 13:30:00', '2021-10-30 14:00:00')
  ;

Subquery to determine overlaps (for debugging purposes)

SELECT
        t1.emp_id,
        t1.task_id,
        t1.time_in,
        t1.time_out,
        (EXTRACT(epoch FROM t1.time_out-t1.time_in)/3600) as task_duration,
         CASE
             WHEN t2.task_id IS NULL THEN 0
             ELSE (EXTRACT(epoch FROM t2.time_out-t2.time_in)/3600)
         END as overlap_duration,
         t2.task_id as overlap_task
    FROM
        task_times t1
    LEFT JOIN
        task_times t2 ON t1.emp_id = t2.emp_id AND
                         t1.task_id < t2.task_id AND
                         (
                      (t1.time_in between t2.time_in and t2.time_out) or
  (t1.time_out between t2.time_in and t2.time_out) or
  (t1.time_in < t2.time_in and t1.time_out > t2.time_out) or
  (t1.time_in > t2.time_in and t1.time_out < t2.time_out)
                      );

Actual Query (I've only including the mins column for debugging purposes)

SELECT
     emp_id,
     task_id,
     MAX(CASE
         WHEN overlap_duration>0 THEN task_duration
         ELSE 0
     END ) + SUM(CASE
         WHEN overlap_duration=0 THEN task_duration
         ELSE 0
     END) - AVG(overlap_duration) as hrs,
     (MAX(CASE
         WHEN overlap_duration>0 THEN task_duration
         ELSE 0
     END ) + SUM(CASE
         WHEN overlap_duration=0 THEN task_duration
         ELSE 0
     END) - AVG(overlap_duration))*60 as mins
FROM (
    SELECT
        t1.emp_id,
        t1.task_id,
        t1.time_in,
        t1.time_out,
        (EXTRACT(epoch FROM t1.time_out-t1.time_in)/3600) as task_duration,
         CASE
             WHEN t2.task_id IS NULL THEN 0
             ELSE (EXTRACT(epoch FROM t2.time_out-t2.time_in)/3600)
         END as overlap_duration,
         t2.task_id as overlap_task
    FROM
        task_times t1
    LEFT JOIN
        task_times t2 ON t1.emp_id = t2.emp_id AND
                         t1.task_id < t2.task_id AND
                         (
                      (t1.time_in between t2.time_in and t2.time_out) or
  (t1.time_out between t2.time_in and t2.time_out) or
  (t1.time_in < t2.time_in and t1.time_out > t2.time_out) or
  (t1.time_in > t2.time_in and t1.time_out < t2.time_out)
                      )
                      
) t3
GROUP BY
    emp_id, task_id
ORDER BY
    emp_id, task_id;

View on DB Fiddle

Let me know if this works for you.