The point on the Wifi connectivity issue in the captive portal Mac login process is that if the process is not successful, either by lack of login, or some other technical problem in the Apple Captive Network Assistant (CNA), it will lose Wifi connectivity.
So, the lack of ping connectivity is a symptom and not a cause.
As it is a fairly common problem with some captive portals, depending on their configuration, I would venture to say you need to take out the hardcoded DNS servers of your DNS configuration.
After you taking them out, it will allow the DHCP request to get Starbuck's own captive DNS portal servers, which will allow the login to proceed.
PS. For instance, FON captive portals from at least of our Telecom operators (NÓS) used to have the very same problem - and behaviour - for years, now they seem to have catch on and just probably inserted firewall rules in the new firmware versions to intercept any non-encrypted DNS requests coming from clients connected via Wifi.
PS2. If you disable the CNA, you will be able to get away at least with pinging the gateway /wifi AP address.
However for opening the authentication portal before authenticating, you will still need to take out your hardcoded DNS addresses first.
PPS for future visitors, using either Mac or Linux, bear in mind: Firefox is capable of dealing with captive portals in it's own. However, some older captive portals will force you to get the DNS servers from their DHCP e.g. won't work with fixed DNS servers/DNS over TLS on your configuration.