SQL Server 2017 (Linux)

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create table agent_events (
 [Event Date] smalldatetime, 
 AGENT varchar(30),
 [Event Type] varchar(30), 
 [Event Subtype] varchar(30)
)
insert into agent_events ([Event Date], AGENT, [Event Type], [Event Subtype]) values
('2022-03-14 09:00', 	'AGENT 1', 	'VOICE CHANNEL', 'LOGIN'), 
('2022-03-14 11:10', 	'AGENT 1', 	'BREAK',        'START'), 
('2022-03-14 11:20', 	'AGENT 1', 	'BREAK', 	'END'), 
('2022-03-14 13:10', 	'AGENT 1', 	'VOICE CHANNEL', 'LOGOUT'), 
('2022-03-14 14:00', 	'AGENT 1', 	'VOICE CHANNEL', 'LOGIN'), 
('2022-03-14 15:50', 	'AGENT 1', 	'BREAK', 	'START'), 
('2022-03-14 16:00', 	'AGENT 1', 	'BREAK', 	'END'), 
('2022-03-14 18:10', 	'AGENT 1', 	'VOICE CHANNEL', 'LOGOUT'), 
('2022-03-14 10:00', 	'AGENT 2', 	'TICKET CHANNEL', 'LOGIN'), 
('2022-03-14 12:00', 	'AGENT 2', 	'BREAK', 	'START'), 
('2022-03-14 12:10', 	'AGENT 2', 	'BREAK', 	'END'), 
('2022-03-14 14:00', 	'AGENT 2', 	'TICKET CHANNEL', 'LOGOUT');
12 rows affected

SELECT AGENT, [Event Type]
, MIN(CASE WHEN [Event SubType] IN ('LOGIN', 'START') THEN [Event Date] END) AS [Event Start] 
, MAX(CASE WHEN [Event SubType] IN ('LOGOUT', 'END')  THEN [Event Date] END) AS [Event End] 
FROM
(
SELECT [Event Date], AGENT, [Event Type], [Event Subtype]
, Rnk = SUM(IIF([Event SubType] IN ('LOGIN', 'START'), 1, 0)) 
        OVER (PARTITION BY AGENT, [Event Type], CAST([Event Date] AS DATE) ORDER BY [Event DATE])
FROM agent_events 
) q
GROUP BY AGENT, [Event Type], CAST([Event Date] AS DATE), Rnk
ORDER BY AGENT, [Event Start];


AGENT
Event Type
Event Start
Event End


AGENT 1
VOICE CHANNEL
2022-03-14 09:00
2022-03-14 13:10

AGENT 1
BREAK
2022-03-14 11:10
2022-03-14 11:20

AGENT 1
VOICE CHANNEL
2022-03-14 14:00
2022-03-14 18:10

AGENT 1
BREAK
2022-03-14 15:50
2022-03-14 16:00

AGENT 2
TICKET CHANNEL
2022-03-14 10:00
2022-03-14 14:00

AGENT 2
BREAK
2022-03-14 12:00
2022-03-14 12:10


Warning: Null value is eliminated by an aggregate or other SET operation.

AGENT	Event Type	Event Start	Event End
AGENT 1	VOICE CHANNEL	2022-03-14 09:00	2022-03-14 13:10
AGENT 1	BREAK	2022-03-14 11:10	2022-03-14 11:20
AGENT 1	VOICE CHANNEL	2022-03-14 14:00	2022-03-14 18:10
AGENT 1	BREAK	2022-03-14 15:50	2022-03-14 16:00
AGENT 2	TICKET CHANNEL	2022-03-14 10:00	2022-03-14 14:00
AGENT 2	BREAK	2022-03-14 12:00	2022-03-14 12:10