On https://accounts.firefox.com/signin there is a link at the bottom for "Use a different account"

But wait!! Do you want to keep the data separate between your regular account and your new account? In that case, you will want to create a work profile first. Let me explain.

If you ever created separate "persons" in Google Chrome or separate "identities" in Internet Explorer, a Firefox profile is similar.

A profile is a distinct Firefox data folder with its own settings, bookmarks, add-ons, etc. Let the profiles be the boss, and think of Firefox accounts as a service a profile can use to share data with other Firefox installations.

To get started:

Inside Firefox, type or paste about:profiles in the address bar and press Enter/Return to load it.

Take a quick glance at the page and make a mental note of which Profile has this notation: This is the profile in use and it cannot be deleted. That is your current default profile.

Click the "Create a New Profile" button, then click Next. Assign a name like Work, ignore the option to relocate the profile folder, and click the Finish button.

Firefox will switch your default profile to the new one, so click the Set as Default Profile button for your regular one to avoid an unwanted surprise at your next startup.

Scroll down to Work and click its Launch profile in new browser button.

Firefox should open a new window that looks like a brand new, uncustomized installation. (Your existing Firefox window(s) should not be affected.)

Do you want to seed this profile with data from your regular profile?

If Yes: you can connect to your existing Firefox Account, allow time for Sync, then disconnect (you can sign out using the menu).

If No: do not connect to your existing Firefox Account.

Now you can create your new Firefox "work" Account and keep it associated with the work profile to avoid accidental crossover.

Make sense?

Do you have other devices connected to the same work account (i.e. do you have more than one work computer) ?

The use case of Sync is syncing data between multiple computers and not the usage as a backup, so with one work computer and one home/personal computer that needs to be separated Sync is of limited use.