Elaborate Serializing and Deserializing of Data

Nobody has claimed this yet.

Some improvements can be made to the serializing and deserializing of data:

- `this.hdk` can/should be serialised and deserialised
- Only the `publicKey` and `chainCode` needs to serialised/deserialised
- Setting `this.hdKey` can be refactored via a `setHdKey` method
- `this.page` and `this.unlockedAccount` should be included in data serialization
- `this.hdPath` can be changed via deserialization without triggering the `this.setHdPath` method
- `implementFullBIP44` is incorrectly serialised
- Should be `implementFullBIP44: this.implementFullBIP44` instead of `implemntFullBIP44: false`
- Some "resetting" of data can be refactored (i.e., see `forgetDevice`, `setHdPath` and the `constructor`)
- Some refactoring for filtering `this.accounts` can be done
- `this.bridgeUrl` can be changed via deserialisation without updating the `iframe` URL
- This should either be only settable via `init`, or should trigger `iframe` deletion and recreation (less desireable)

Start by tracing the constructor, serialization and deserialization paths, then inspect forgetDevice, setHdPath, init, and the iframe handling mentioned in the issue. Verify that the listed state fields round-trip correctly, the implementFullBIP44 key is preserved, account filtering is consistent, and bridgeUrl changes follow the chosen lifecycle behavior.

Written by the indexing model from the issue text.