You can use below regex:
| rex field=<FIELD_NAME> "\[0:(?<id>[a-z0-9]+)@(?<name>[a-z@.]+) 0\]"
Test query:
| makeresults | eval test="[01/05/2020 13:06:21] BAUAJM_I_30031 Client [CA WAAE Auto:15515][5][
[email protected]:50019:12.304.593.10] [0x80c91100][02/05/2020 13:06:21.8474][0:
[email protected]@hostname.com 0] API ID [34] execution started.&[01/05/2020 13:06:21] BAUAJM_I_30032 Client [CA WAAE Auto:15509][5][
[email protected]:12345:19.304.293.10] [0x28bbbfff][02/05/2020 13:06:21.6946][0:
[email protected]@hostname.com 0] API ID [66] execution completed. Total time: 0.132519 seconds." | makemv delim="&" test | mvexpand test | rex field=test "\[0:(?<id>[a-z0-9]+)@(?<name>[a-z@.]+) 0\]" | table id, name, test
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