Improve logging in start.sh

[mathbunnyru]

Possible future improvements (just a note for someone, who will want to improve our docker stacks):

1. Test JUPYTER_DOCKER_STACKS_QUIET env variable
2. Always add log_level like this: `_log "INFO" "my_message"
3. Based on the log level color can be added
4. Exit on fatal errors (or maybe just errors)
5. Add timestamps, like INFO[2021-08-23 11:00:00.000000] my_message
6. Stop using bash, haha 👍

Based on comment: #1526 (review)

[yuvipanda]

@mathbunnyru I think this should still stay open for a while?

[mathbunnyru]

Sure, reopened.