The first part of what I wrote regarding the Chrome ID was just rubbish, I just edited the text.

The Chrome ID I was referring to is more accurately named: "Current Chrome Profile Serial Number" and is automatically listed when purchasing a license key (try it out with a different profile. (What I wrote before was rubbish, as it is the ID of the profile, not Chrome itself (just checked it again on two PCs to be sure).
It says also "This number must be filled automatically by Tabs Outliner, please don't change or edit it. It will be embedded in the license key and used to validate it against your Chrome Profile.".

What is true though is that when you use TO on >1 machine witih the same profile, you wll have >1 local backup directory. So, restoring the history on another machine than the last one used to make a backup will almost surely lead to a loss of data. This is a connected issue (backup-restore), but different problem though (>1 machines wanting to make us of the same TO database).

Regarding the email address: it is not inconsistent, but you should be aware of it. I linked my cc to one gmail address, but wanted to purchase it for the profile using another gmail address. Obviously the license key and URL is linked to the latter, although the mail with the URL is sent to the former email address.

Happened twice yesterday, had to repair it twice, reentered the license key URL in the original purchase mail (made it a bookmark in the meanwhile as I expect no changes on the short term). All local backups were gone unfortunately, but gdrive backups were there.
I recommend to make frequent, manual backups after big reorgs or changes of the tree.

<Edited:  rubbish removed.>

NB: the mail used for receipt of the license key does NOT have to be the same as the gmail address linked to that particular Chrome profile (In my case, it isn't, and it works without a prob)