Okay, after weeks of searching through sketchy websites and the Internet Archive, I finally managed to get both fingerprint software and Bluetooth working!
I noticed on the data sheet for this model that it said the following:
Superior access protection via integrated fingerprintsensor, SmartCard reader and SmartCase™Logon+software
So the search began for SmartCase Logon+. Only handful of websites mentioned it, so I decided to give Internet Archive a try. Looking through a just a handful of uploaded old recovery images, I found two that included SmartCase software. Here's the one that worked
After installing it, I was finally able to successfully enroll a fingerprint, and enable OS Logon for it.
As for Bluetooth software, it seems Toshiba's BT stack was included software. For this, I also used the Internet Archive. It installed without issues and works well. I will leave this post for anyone looking for this obscure (and unfortunately less available) software.