Processing method:

/bin/bash -x dump.sh > trace.log 2>&1

Reason:
Trace it with strace

strace /bin/bash -x dump.sh

Result:

write(2, "+ idx=1\n", 8+ idx=1
)                = 8
rt_sigprocmask(SIG_BLOCK, NULL, [], 8)  = 0
write(2, "+ echo 1\n", 9+ echo 1
)               = 9
write(1, "1\n", 21
)                      = 2
rt_sigprocmask(SIG_BLOCK, NULL, [], 8)  = 0
read(255, "", 29)                       = 0
exit_group(0)                           = ?

It can be seen that +idx=1 and +echo1 are write(2,), which is the standard error output. Although it is displayed on the screen, > this content will not be written to the file by default.
The following command can redirect standard error to 1

/bin/bash -x dump.sh > aa 2>&1

In the man bash manual chapter: CONDITIONAL EXPRESSIONS, -x means:

-x file
    True if file exists and is executable.

parameter -x will list the order in which the shell executes statements and print them. +echo 1This kind of statement is not the output of the script, so it cannot be saved to a file.

-ｘDebug mode