TL;DR: Insert "bash" before the script in crontab and in any scripts called by the script.
I have a fix for this. None of the previous answers worked for me. I have two Asus laptops running Kubuntu (updated to kernel v5.8) with virtually identical configurations. I don't know why one has the problem and the other doesn't. However, after 2 days of experimentation I found a fix. Hopefully, someone more knowledgeable than I can find the cause.
Cron is using sh instead of bash. I tried adding SHELL=/bin/bash and defining PATH above the commands in crontab and it had no effect. All of my scripts have the #!/bin/bash shebang at the beginning, also with no effect. My scripts' (and their directories') permissions are 777. The scripts don't run for cron or users, no matter what combination of user:group I tried on the files. Using full pathnames is cron and inside the scripts had no effect that was different from using environment variables.
My fix was to insert "bash" before the script filename in crontab. E.g.:
00 01 * * * bash $BASH_SCRIPTS/backup_os.sh
(Yes, cron has no problem with using my environment variables defined in /etc/environment.) Also, in cron, when a script runs another script, the second script will get "permission denied" unless that script is modified to have "bash" before the 2nd script's filename, or use "source" if that'll work with your script.