I sent in a support request and received this message:
In order to receive the 100 emails per day, you'll need to choose the
Email API trial or the Marketing Campaigns trial. You can do so by
navigating to Settings > Account Details > Your Products > Start Trial to Send More.
If you start the trial you will receive 40,000 emails a month, but
just for 30 days. Once your 30 day trial period has expired, you will
be able to send only up to 100 emails per day (unless you choose to
upgrade your account).
If you don't start the trial you will be limited to send only 100
emails a month.
On short, you are now able to send only 100 emails a month, and if you
start the trial you will be able to send up to 40,000 emails in the
first month and 100 emails a day from that point onwards.
So in other words, when you first create your account, it starts out at only 100 emails per month, but you can fix that by starting the trial.
I gave that a shot and now it works as expected.
Note that you're not required to give them your credit card details to sign up for the trial, so there doesn't appear to be any downside to doing so.
I'm not sure why the account doesn't default to 100/day from the beginning. I guess their goal is to make you more interested in their paid plan.