Comment 1 for bug 2004223

Yes there is a way :) Install a plugin like Firefox Containers (https://support.mozilla.org/en-US/kb/containers) and keep your work and personal profiles entirely separate with independent cookie jars.

If your entry point is Google, we don't have a lot of control on whether they consider you as "logged in as @canonical.com but with stale credentials" and send you to Ubuntu SSO to log in, before giving you a chance to switch profiles.