How could I update the session expired / timeout message?
Thanks in advance!

You can modify the translation file or create your own - www.limesurvey.org/manual/Translating_LimeSurvey

I have created a survey which base language is English. I have added Traditional Chinese (HK) as additional language.
I clicked the survey link which default language is Traditional Chinese (HK) . I left the survey idle for a while and clicked submit button.
The session timeout message appeared. However it is in English instead of Traditional Chinese (HK).

Is language of session expired message depending on base language instead of language selected?
Thanks!

In my opinion, all messages received by a respondent should be in the current survey language. If not, please file a bug report.

However, Chinese (HK) is only 40% translated, so actually it could be because of that as well.

But I did a quick check and the "We are sorry but your session has expired." seems to be translated: 很抱歉，您的會話已過期。

Yes, I have checked there is translation in Chinese (HK) for session expired message.

I have created another survey which base language is Chinese (HK) and English is additional language.
I found that the session expired message is in English when I selected Chinese (HK) as survey language.
Thus it seems it follows the base language rather than survey language.

Please file a bug report and post a link here.