What worked for me is the following configuration:
crontab:
0 4 * * * /opt/script/cypress.sh > /opt/log
cypress.sh:
#!/bin/sh
. $HOME/.bashrc
cd "/opt/Website Testing/" && "/opt/Website Testing/node_modules/.bin/cypress" run --record --key *
Thanks for your help, the ". $HOME/.bashrc" was missing for me.