Your request is not related to tesseract specifically but Visual studio and Dot.Net.
I am not familiar with Dot.Net and publishing/deploying if it's the final product. Anyway, the error message indicates that your application is not able to find its dependency (leptonica-1.80.0.dll).
So, first of all, you need to learn the dependencies of your application (your message "I tried installing x86: vc_redist.x86.exe..." indicates you have no clue about it).
Next, you need to understand what are system or general dependencies (e.g. usually you can not distribute content of vc_redist.x86.exe or Dot.net - user has to install them by himself) and what are specific dependencies you need to install/package with your app (e.g. leptonica). Location of specific dependencies depends on your OS, used framework, or other tools (tesseract/leptonica wrapper in this case) - you need to find out where they look for external libraries.
Tools like
https://www.dependencywalker.com/ can help you, but I think it would be wise to take some lessons about tools you decided to use and how to produce the final product (application) with them.