Учитывая, что Вы хотите удалить все снаружи, сначала [и последний]:
sed 's/^[^[]*//;s/[^]]*$//'
Тест:
$ cat out.file
Obj^A^D^Vavro.schema<88>^L{"type":"record","name":"NiFi_ExecuteSQL_Record","namespace":"any.data","fields":[{"name":"FEED_SEQUENCE","type":["null",{"type":"bytes","logicalType":"decimal","precision":38,"scale":0}]},{"name":"FEED_UNIQUE_NAME","type":["null","string"]},{"name":"COUNTRY_CODE","type":["null","string"]},{"name":"EXTRACTION_TYPE","type":["null","string"]},{"name":"PROJECT_SEQUENCE","type":["null",{"type":"bytes","logicalType":"decimal","precision":38,"scale":0}]},{"name":"CREATED_BY","type":["null","string"]},{"name":"CREATED_DATE","type":["null",{"type":"long","logicalType":"timestamp-millis"}]},{"name":"UPDATED_BY","type":["null","string"]},{"name":"UPDATED_DATE","type":["null",{"type":"long","logicalType":"timestamp-millis"}]},{"name":"FEED_DESC","type":["null","string"]}]}^Tavro.codec^Hnull^@àÂ<87>)[ù<8b><97><90>"õ^S<98>[<98>±
$ sed 's/^[^[]*//;s/[^]]*$//' out.file
[{"name":"FEED_SEQUENCE","type":["null",{"type":"bytes","logicalType":"decimal","precision":38,"scale":0}]},{"name":"FEED_UNIQUE_NAME","type":["null","string"]},{"name":"COUNTRY_CODE","type":["null","string"]},{"name":"EXTRACTION_TYPE","type":["null","string"]},{"name":"PROJECT_SEQUENCE","type":["null",{"type":"bytes","logicalType":"decimal","precision":38,"scale":0}]},{"name":"CREATED_BY","type":["null","string"]},{"name":"CREATED_DATE","type":["null",{"type":"long","logicalType":"timestamp-millis"}]},{"name":"UPDATED_BY","type":["null","string"]},{"name":"UPDATED_DATE","type":["null",{"type":"long","logicalType":"timestamp-millis"}]},{"name":"FEED_DESC","type":["null","string"]}]