Hey there! Celine from the Community Support team at Figma here.Thanks for flagging this, and I understand the urgency given the site is live for your medical practice.
Custom domains for Figma Sites are a paid-plan feature (Professional, Organization, or Enterprise). The Education plan lets you publish your site, but only on the default figma.site subdomain (connecting a custom domain isn't included, which is why the option wasn't available before.) This is a limitation of the Education plan rather than a bug, so nothing was suddenly "lost". The feature simply wasn't part of the Education plan to begin with.
The good news is your domain isn't wasted, it just needs the site to be on a paid plan for the option to appear. Since you've already upgraded to a Professional Full seat, the "Add connected domain" option should now be available in your Domains settings (Professional supports up to 10 custom domains). Since it's still not showing up after the upgrade, I'd like our team to take a closer look at your account directly, given the urgency here.
I've gone ahead and created a support ticket on your behalf flagging this as time-sensitive due to a live client site being down, and the team will follow up with you directly as soon as possible. For reference, your support case is #2084784, sent to your email address: axxxxo@uxxxc.exxxu. Feel free to add any additional details via the support ticket, and continue the conversation there, thank you!