Hi - I signed up for the Lightroom with 1TB plan and it shows that it's version 3.4? Is that correct? Isn't that an older version?
Sorry about the confusion caused. It seems that you hae installed Lightroom Desktop not Lightroom Classic that you are looking for.
Please open the Creative Cloud Desktop app and install Lightroom Classic(latest version 9.4)
The Lightroom Desktop 3.4 is the latest version and it is the new cloud-based photo service that works across desktop, mobile, and web. Lightroom Classic is the desktop-focused digital photography product.
For more details, see Lightroom Classic vs Lightroom Desktop
The 'Lightroom 1TB' plan does not include Lightroom-Classic v9.4 (as advised by Akash)
You would need to contact Adobe and request a change to the Photography Plan (20GB) to have Lr-Classic available in your CC Desktop App.
Lightroom-Classic does require a subscription to the Photography (20Gb) Plan. (12 months- paid monthly or annually)
All "licensing" (activation), and installs are controlled by the Adobe Creative Cloud Desktop App that you install.
Then for the plan that you signed up for, version 3.4 is the current version. Your images are stored in the cloud. That's why you have 1 TB of cloud storage.