Exploration of bash interactivity, SHLVL and `-t 1` values in various forms of invocation

tst.sh

#!/usr/bin/env bash

case "$-" in
  *i*) echo 'interactive'  ;;
  *) echo 'non-interactive'  ;;
esac
echo "SHLVL = $SHLVL"
[[ -t 1 ]] && echo "tty STDOUT? : true" || echo "tty STDOUT? : false"

tstl.out

$ ./tstl.sh 
Sourcing a script
source ./tst.sh :
non-interactive
SHLVL = 2
tty STDOUT? : true

Invoking a script
./tst.sh :
non-interactive
SHLVL = 3
tty STDOUT? : true

Invoking a script within a string
echo `./tst.sh` :
non-interactive SHLVL = 3 tty STDOUT? : false

Sourcing a script within a subshell
( source ./tst.sh ) :
non-interactive
SHLVL = 2
tty STDOUT? : true

Invoking a script within a subshell
( ./tst.sh ) :
non-interactive
SHLVL = 3
tty STDOUT? : true

Invoking a script within a string within a subshell
( echo `./tst.sh` ) :
non-interactive SHLVL = 3 tty STDOUT? : false

Evaluating a script invocation within a string
eval "echo \`./tst.sh\`" : 
non-interactive SHLVL = 3 tty STDOUT? : false

Evaluating a script invocation within a string, in a subshell
( eval "echo \`./tst.sh\`" ) :
non-interactive SHLVL = 3 tty STDOUT? : false

tstl.sh

#!/usr/bin/env bash

prog=./tst.sh

echo "Sourcing a script"
echo "source $prog :"
source $prog

echo ''
echo "Invoking a script"
echo "$prog :"
$prog

echo ''
echo "Invoking a script within a string"
echo "echo \`$prog\` :"
echo `$prog`

echo ''
echo "Sourcing a script within a subshell"
echo "( source $prog ) :"
( source $prog )

echo ''
echo "Invoking a script within a subshell"
echo "( $prog ) :"
( $prog )

echo ''
echo "Invoking a script within a string within a subshell"
echo "( echo \`$prog\` ) :"
( echo `$prog` )

echo ''
echo "Evaluating a script invocation within a string"
echo "eval \"echo \\\`$prog\\\`\" : "
eval "echo \`$prog\`"

echo ''
echo "Evaluating a script invocation within a string, in a subshell"
echo "( eval \"echo \\\`$prog\\\`\" ) :"
( eval "echo \`$prog\`" )