Direct mode key stored in mozc::client::Client may not be updated upon config change

## Description
I'm coming from https://github.com/fcitx/mozc/issues/62 but it seems that this is an issue in mozc's code

direct_mode_keys_ in client.cc (https://github.com/google/mozc/blob/14afac9728dd3f04e3d73633f4fa925d38589368/src/client/client.cc#L112) is only updated on:
1. constructor
2. SetConfig

That makes this option is not updated correctly when changing from mozc_tool at runtime. I wonder, if there's a way to allow engine to refresh this changes or detect whether the config is updated? (A.k.a, if there is a way for me to write some code in fcitx to do the right thing)

## Steps to reproduce
Change direct mode related key
Use it in client

## Expected behavior
Change to direct mode key is updated.

## Actual behavior
Direct mode key remains unchanged until engine restart.

## Screenshots

## Version or commit-id
Mozc-2.31.5712.102+24.11.oss

## Environment
- OS: Arch linux
- IMF (for Linux) Fcitx5, but probably not relevant.
- Related Applications [e.g. Chromium 109, gedit, etc]

## Investigations
- Whether this issue happens on both Ibus and other IMF (e.g. Fcitx, uim).
+ yes, no, N/A
- Whether this issue happens on other IMEs (e.g. Anthy, SKK).
+ yes, no, N/A
- What applications this issue happens on (e.g. Chromium, gedit).
+ list of applications
- What applications this issue does not happen on (e.g. Chromium, gedit).
+ list of applications, or not-found
- (optional) What versions or commit-ids this issue did not happen on
(e.g. Mozc-2.28.4960.100+24.11.oss).
+ list of versions or commit-ids, or no-investigation.

## Additional context
Add any other context about the problem here.