Are you using an extension like Alby?

If not, clearing application data should do it:

1. Visit primal.net
2. Right click on page
3. Choose "inspect"
4. Find the tabs: Elements, Console, Sources .....
5. Find the Application tab (you might need to click the >> button to see more tabs)
6. In the left section, choose "Storage" inside the Application section (after Manifest and Service Workers)
7. In the main section, find "clear site data"
8. Tick all the boxes underneath the button
9. Click the clear site data button.

If you wanted to be more surgical about it, it SEEMS like they keep all their data in "localStorage" only for now. 

 You can do these steps for any website to make it forget about you.

Of course, this isn't foolproof agains servers surveilling you. They will use your IP address AND... a "browser fingerprint" where they run random things to time the speed of your hardware and sniff changes in configuration to bud a unique fingerprint that they can always recalculate. Like as if your computer was a signing device and they could always pull out your public key to identify you.

This is why I use Brave... Brave thwarts this fingerprint attack.

See: https://brave.com/privacy-updates/3-fingerprint-randomization/