The text on your pic looks the same as the one in your script, yes. But it's a bit hard to be sure from just a pic.
But note how the text comes to your terminal when you run the script? The command substitution is supposed to capture the output, whatever gets caught by it, does not get printed.
adb probably prints that message to the standard error, not standard output, so it doesn't get caught.
You could verify that with something like this:
echo "running the command substitution... (errors would print after this line)"
output=$(adb shell getprop sys.boot_completed)
echo "captured output (stdout): '$output'"
Then see what comes out where.
And if that's indeed the problem, then you need to redirect the stderr to stdout in the command substitution:
if [[ "$(adb shell getprop sys.boot_completed 2>&1)" =~ "adb: no devices/emulators found" ]]; then