What is the meaning of the number in the upper-right corner of the Watchtower screen?

Login/site count alone I doubt would influence the score. Just because User A has 10 passwords at all their best rating and User B has 20 passwords all at their best rating, it doesn't make User B any better than User A security wise. Arguably you could say User B has more exposure with their information being in 10 more accounts, but in the context of 1Password rating security aspects, the calculation is more likely to involve:

• Password strength being the highest possible rating for each site
• 2FA being enabled (if matched against watchtower 2FA lookup)
• Not a re-used password

My additional thoughts:

• Sites enabled for two-factor authentication that don't match against Watchtower might not influence the score, but obviously still worth enabling. It is important to go through all sites as Watchtower does not always know 2FA is available for lesser known sites or discussion boards
• Changing passwords that are rated lower like Weak/Good or possibly Very Good will increase the score quicker than compared to going from Excellent to Fantastic as a password rating.

Ultimately, it's just a visual indication of your password health and 2FA coverage and the number itself is meaningless, much like your credit score represented as a number. The number is a representation, the actual detail that credit agencies look at is the history and markers. For watchtower, it's password strength, 2FA and any weak password identified in one place.

Aiming for unique passwords with a strength of excellent/fantastic with 2FA enabled where possible, you'll be well covered. Even having fantastic on all password is probably overkill for realistic brute forcing.