Postgres 13

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WITH RECURSIVE
  d1 (id, parent_id, name) as (
    values
      (1, null, 'A'),
      (2, null, 'B'),
      (3,    1, 'A1'),
      (4,    3, 'A1a'),
      (5,    3, 'A1b'),
      (6,    2, 'B1'),
      (7,    2, 'B2')
  ),
  d2 AS (
    SELECT d1.*, 0 AS level
    FROM d1
    WHERE parent_id IS NULL
    UNION ALL
    SELECT d1.*, d2.level + 1
    FROM d1
    JOIN d2 ON d2.id = d1.parent_id
  ),
  d3 AS (
    SELECT d2.*, jsonb_build_array() children
    FROM d2
    WHERE level = (SELECT max(level) FROM d2)
    UNION (
      SELECT (branch_parent).*, jsonb_agg(branch_child)
      FROM (
        SELECT branch_parent, to_jsonb(branch_child) - 'level' - 'parent_id' AS branch_child
        FROM d2 branch_parent
        JOIN d3 branch_child ON branch_child.parent_id = branch_parent.id
      ) branch
      GROUP BY branch.branch_parent
      UNION
      SELECT d2.*, jsonb_build_array()
      FROM d2
      WHERE d2.id NOT IN (
        SELECT parent_id FROM d2 WHERE parent_id IS NOT NULL
      )
    )
  )
SELECT jsonb_pretty(jsonb_agg(to_jsonb(d3) - 'level' - 'parent_id')) AS tree
FROM d3
WHERE level = 0;

tree
[ { "id": 2, "name": "B", "children": [ { "id": 6, "name": "B1", "children": [ ] }, { "id": 7, "name": "B2", "children": [ ] } ] }, { "id": 1, "name": "A", "children": [ { "id": 3, "name": "A1", "children": [ { "id": 4, "name": "A1a", "children": [ ] }, { "id": 5, "name": "A1b", "children": [ ] } ] } ] } ]