This is the reason why (FRAUD ALERT) is there to secure e-commerce... they will proxy the payment using your (FRAUD ALERT) account and not disclose your CC details to stores that can accept their payments.
If you need to use your credit cards, contact the FI issuing it and ask if they would offer you SMS notifications for any purchase.
You will be notified quickly of any transaction and have a considerable time window to react.
There are so many different points of compromise that can could lead to what has been described by the OP.
The employee workstation might be compromised by malware, the website where payments are being entered, your phone, a malicious employee.... the list goes up and I don't plan to educate anyone over the topic.
In regarding the uber eats transactions.. this is likely someone checking if the stolen CC information works to verify if the transaction will work against controls are know to block fraudulent payments. (small amounts and same area codes)
Expect the heavy ones to come after these "low value testing transactions - e.g. uber eats" ... if you don't react quickly.
Be a good citizen and contact the store informing what is happening.
The more victims do the same, the easier will be to identify where the problem is and you will also save yourself from any wrongdoing by informing law enforcement that you have become a victim of fraud.
Inform your FI and let they know your CC data was compromised, they will likely revoke your card number and issue a new one.. at no cost.
