Manipulate spool command output in Bash Scripting

This isn't really a shell question, but in your heredoc, before the spool, add some SQL*Plus formatting commands; e.g.:

/usr/lib/oracle/12.2/client64/bin/sqlplus -s esg/esg << EOF
set feedback off
set pagesize 0
set trimspool on
spool /tmp/test
...

Setting pagesize to zero "suppress[es] all headings, page breaks, titles, the initial blank line, and other formatting information".

Setting feedback off removes all feedback like '10 rows selected'.

There is a summary of the set commands in the documentation. There is also a section on formatting SQL*Plus reports.

I recommend using Alex's solution - but if you do want all that output in your spool log, and just want to strip out the relevant bits for something else, try sed, which will allow layers conditions.

$: sed -n '/^---/,/^$/{ /^[A-Z]/p }' test
TEMP_TBS1                  23
SYSAUX                     4
GTEMP                      3
SYSTEM                     3
UNDOTBS2                   0
UNDOTBS1                   0
TEMP                       0
USERS                      0
DATA_TBS1                  23
INDEX_TBS1                 11

Breaking that down:

sed -n says don't print anything unless explicitly ordered.
/^---/,/^$/ says do the following command on lines in this range only.
{ ... } says apply the contents of the braces when the previous conditions apply, so since the previous condition was a range select, this allows multiple commands to be executed collectively on each line in the range.
/^[A-Z]/p says print only if the first character is a capital letter.

Collectively, all this says "for lines between dashes and a blank line, print if and only if they begin with a capital letter". Everything else will be ignored.