error: invalid input syntax for type json postgreSQL NodeJS

You're missing the quotes around the JSON strings. This should work:

await this.db.query(
  `UPDATE guest_group
  SET custom_fields = jsonb_insert(custom_fields, '{0}', '{"value": $3, "display_name": "Traces", "servicio_tags": ["trace"]}'::jsonb, true)
  WHERE '{"value": $1}' <@ ANY(
  SELECT el
  FROM jsonb_array_elements(custom_fields) AS el
  WHERE el->'servicio_tags' = '["full-name"]'::jsonb)
  AND '{"value": $2}' <@ ANY(
  SELECT el
  FROM jsonb_array_elements(custom_fields) AS el
  WHERE el->'servicio_tags' = '["room-number"]'::jsonb)`,[
   JSON.stringify(trace.guestName),
   JSON.stringify(trace.guestRoomNumber),
   JSON.stringify(trace.value)
]);

However, I would rather pass whole JSON(B) values to the query, and let node-pg do the escaping:

await this.db.query(
  `UPDATE guest_group
  SET custom_fields = jsonb_insert(custom_fields, '{0}', $3::jsonb, true)
  WHERE $1 <@ ANY(
  SELECT el
  FROM jsonb_array_elements(custom_fields) AS el
  WHERE el->'servicio_tags' = '["full-name"]'::jsonb)
  AND $2 <@ ANY(
  SELECT el
  FROM jsonb_array_elements(custom_fields) AS el
  WHERE el->'servicio_tags' = '["room-number"]'::jsonb)`,[
   {"value": trace.guestName },
   {"value": trace.guestRoomNumber },
   {"value": trace.value, "display_name": "Traces", "servicio_tags": ["trace"]}
]);

Or using the other query:

await this.db.query(
  `UPDATE guest_group
  SET custom_fields = jsonb_insert(custom_fields, '{0}', $3::jsonb, true)
  WHERE EXISTS (
    SELECT 1
    FROM jsonb_array_elements(custom_fields) AS el
    WHERE el->>'value' = $1
      AND el->'servicio_tags' = '["full-name"]'::jsonb)
  AND EXISTS (
    SELECT 1
    FROM jsonb_array_elements(custom_fields) AS el
    WHERE el->>'value' = $2
      AND el->'servicio_tags' = '["room-number"]'::jsonb)
`, [
   trace.guestName,
   trace.guestRoomNumber,
   {"value": trace.value, "display_name": "Traces", "servicio_tags": ["trace"]}
]);