refactor(dock): simplify badge count logic

[kovsu]

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[Innei]

/ai-review

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Suggested PR Title:

refactor(dock): simplify badge count logic

Change Summary: Refactor dock badge logic for cleaner badge count handling.

Code Review: No change requests necessary.

[kovsu]

I only subscribe to a few feeds, and a few moments after I marked all of them as read, hundreds of new ones appear. So will there be a situation where the number will be thousands or even more? It's maybe strange in this situation.

[Przeblysk]

Agree that it makes more sense to show the actual numbers

[Innei]

Perhaps we can limit a relatively large number, such as the unread count not exceeding five digits.