Tweaks to DB API, improved abstractions for better testability.

[bwaresiak]

Please review the release process for BrowserServicesKit here.

Required:

Task/Issue URL: https://app.asana.com/0/856498667320406/1207875839908777/f iOS PR: https://github.com/duckduckgo/iOS/pull/3143 macOS PR: https://github.com/duckduckgo/macos-browser/pull/3033 What kind of version bump will this require?: Major

Description:

Tweak code to improve error handling and events propagation in Clients. Add protocols for improved testability.

Steps to test this PR:

See platform PRs.

OS Testing:

• [ ] iOS 14
• [ ] iOS 15
• [ ] iOS 16
• [ ] macOS 10.15
• [ ] macOS 11
• [ ] macOS 12

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Internal references:

Software Engineering Expectations Technical Design Template