You were right, the only remains of your Windows installation is the (U)EFI partition at the beginning of the disk (vfat). The other two partitions are Ubuntu (ext4) and a swap partition. You can see it here:
Partition Start Sector End Sector # of Sectors System
/dev/sda1 2,048 1,050,623 1,048,576 EFI System partition
/dev/sda2 1,050,624 1,448,605,695 1,447,555,072 Data partition (Linux)
/dev/sda3 1,448,605,696 1,465,147,391 16,541,696 Swap partition (Linux)
I'm not sure what your question is from this point, but if you haven't made a back-up of your personal data from your Windows partition, then it will be very hard (or impossible?) to recover anything, however others might know more about data recovery than I do. (If that is your question, please make it clearer in your description.)
However, if you want to reinstall Windows, you should be able to do so from an installation drive. It is usually considered harder or riskier to install Windows on top of Ubuntu, but if you manage your partitions carefully and recover GRUB at the end of the installation process, you should be able to get the job done.
To manage your partitions before installing Windows, I suggest using GParted on a live session. See this AskUbuntu question on managing partitions with GParted : How to resize partitions?
Also, for the final step, see this article on recovering GRUB: https://help.ubuntu.com/community/Grub2/Installing#Reinstalling_GRUB_2