I don't know if this will help you, but I figured I would post this in the hopes that I may be able to help someone. I came across this solution when I was looking to recover tabs that had been permanently closed after my browser crashed one day. In order to access the information you require, you need to be rooted and have a file explorer app that can access the root files installed on your device. ES File Explorer or Root Explorer are my recommendations.
If you navigate to the root folder of your device (the protected system partition), select DATA, then com.android.chrome. There are several places where you may find information about your current tabs. The first folder to check is app_tabs then 0. In this folder there should be a file called tab_state which contains a list of all your current tabs. There are also other files in this folder called tab3 tab4 etc that contain info about current tabs. I think you need a special text editor / sql editor to read the content of some of these files as the encoding is different. Next place to look is /data/com.android.chrome/app_chrome/Default/. In this folder you'll find a file called History. Depending on your situation, you may find a good list of recent site visits here. Finally navigate to the Sync Data folder. In here you will find the information that's being synced to Google (and this should include all the tabs you currently have synced on other devices). In this file, SyncData.sqlite3, you'll also find a history of all your Google searches (which I sometimes find to be an interesting read). You'll need an sqlite3 data browser app or program on your Pc in order to read this file. The app should be able to export to a highly usable CSV or XLS file that you can open in MS Excel. Hope this helps someone!