SQLite 3.27

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CREATE TABLE tbl (`name` VARCHAR(5), `date_col` TEXT, `value` FLOAT);
INSERT INTO tbl (`name`, `date_col`, `value`) VALUES
  ('NAME6', '2021-06-29', '71'),
  ('NAME7', '2021-06-29', '80'),
  ('NAME1', '2021-06-29', '2925'),
  ('NAME4', '2021-06-29', '182.0'),
  ('NAME2', '2021-06-29', '365'),
  ('NAME3', '2021-06-29', '81.0'),
  ('NAME5', '2021-06-29', '0.25'),
  ('NAME7', '2021-06-27', '81.0'),
  ('NAME1', '2021-06-27', '3000'),
  ('NAME5', '2021-06-01', '0.35'),
  ('NAME6', '2021-06-01', '68.0'),
  ('NAME5', '2021-06-28', '0.15');
SELECT name, date_col, value 
FROM (
  SELECT *, ROW_NUMBER() OVER (
              PARTITION BY name 
              ORDER BY date_col < '2021-06-28' DESC,
                       abs(strftime('%s', date_col) - strftime('%s', '2021-06-28'))
                       
            ) rn
  FROM tbl
)
WHERE rn = 1
ORDER BY name;


name
date_col
value


NAME1
2021-06-27
3000

NAME2
2021-06-29
365

NAME3
2021-06-29
81

NAME4
2021-06-29
182

NAME5
2021-06-01
0.35

NAME6
2021-06-01
68

NAME7
2021-06-27
81


SELECT t1.name, t1.date_col, t1.value 
FROM tbl t1
WHERE t1.date_col = (
  SELECT t2.date_col 
  FROM tbl t2
  WHERE t2.name = t1.name 
  ORDER BY date_col < '2021-06-28' DESC,
           abs(strftime('%s', t2.date_col) - strftime('%s', '2021-06-28'))
  LIMIT 1
)
ORDER BY name;


name
date_col
value


NAME1
2021-06-27
3000

NAME2
2021-06-29
365

NAME3
2021-06-29
81

NAME4
2021-06-29
182

NAME5
2021-06-01
0.35

NAME6
2021-06-01
68

NAME7
2021-06-27
81

name	date_col	value
NAME1	2021-06-27	3000
NAME2	2021-06-29	365
NAME3	2021-06-29	81
NAME4	2021-06-29	182
NAME5	2021-06-01	0.35
NAME6	2021-06-01	68
NAME7	2021-06-27	81