Fix types and add a test for flexible sync client reset

[tomduncalf]

What, How & Why?

I wanted to confirm this was working after a question from the docs team. It turns out our TS definition to only allow "manual" mode was a bit incorrect so I fixed it, and added a simple test which replicates the PBS one in the old tests

☑️ ToDos

• 📝 Changelog entry
• 📝 Compatibility label is updated or copied from previous entry
• 🚦 Tests
• 🔀 Executed flexible sync tests locally if modifying flexible sync
• 📦 Updated internal package version in consuming package.jsons (if updating internal packages)
• 📱 Check the React Native/other sample apps work if necessary
• 📝 Public documentation PR created or is not necessary
• 💥 Breaking label has been applied or is not necessary

If this PR adds or changes public API's:

• typescript definitions file is updated
• jsdoc files updated
• Chrome debug API is updated if API is available on React Native

[tomduncalf]

Merging this as it is a recreated #4702 (created to test out if it was my code making Catalyst CI fail somehow, but it seems to just be pure chance)