In general, basic enumeration on Linux can be done by just uploading & running linPEAS or LinEnum, but here are some commands to run if the scripts aren’t available:

ls -lahR ~
cat /etc/issue
uname -a
lsb_release -a
cat /proc/version
env
netstat -plunt
ss -plunt
cat /etc/fstab
cat ~/.bash_history
cat ~/.bashrc
ps axjf

Also check out pspy to monitor processes without having root, which can help you spot interesting cronjobs/systemd timers, sensitive information exposed via cmdline, etc.