SQL Server 2019

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WITH yourTable AS (
    SELECT 'Student 1' AS Name, '2022-01-01' AS Date, 'false' AS Present UNION ALL
    SELECT 'Student 1', '2022-01-02', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-03', 'true'  UNION ALL
    SELECT 'Student 1', '2022-01-04', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-05', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-06', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-07', 'true'  UNION ALL
    SELECT 'Student 1', '2022-01-08', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-09', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-10', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-11', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-12', 'true'  UNION ALL
    SELECT 'Student 1', '2022-01-13', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-14', 'false' UNION ALL
    SELECT 'Student 1', '2022-01-15', 'true'
),
cte AS (
    SELECT *, ROW_NUMBER() OVER (PARTITION BY Name ORDER BY Date) rn1,
              ROW_NUMBER() OVER (PARTITION BY Name, Present ORDER BY Date) rn2
    FROM yourTable
),
cte2 AS (
    SELECT Name,
           COUNT(CASE WHEN Present = 'false' THEN 1 END) AS num_consec_absent
    FROM cte
    GROUP BY Name, rn1 - rn2
)

SELECT Name,
       COUNT(CASE WHEN num_consec_absent = 2 THEN 1 END) AS Count_2_Consecutive_Absences,
       COUNT(CASE WHEN num_consec_absent > 2 THEN 1 END) AS Count_3_or_more_Consecutive_Absences,
       SUM(num_consec_absent) AS Total_Absences
FROM cte2
GROUP BY Name;

Name	Count_2_Consecutive_Absences	Count_3_or_more_Consecutive_Absences	Total_Absences
Student 1	2	2	11

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