Is there any way to load a file (of extensions .bat or .HTML) into a microcontroller and make the microcontroller run the file when it is connected to a PC using UART
This is a nonsensical question, even if it were actually written as a question.
Microcontrollers run their native instructions. They can't run anything else. Stop and actually think about what you are asking.
BAT files are scripts, or at best interpreted code. That means there is a separate program that reads the code and performs the actions specified by that code. Normally that program is CMD.EXE running on the Windows operating system. First, no microcontroller comes with the equivalent of CMD.EXE built in somehow. Second, even if you were to try doing that yourself, you'd need to port much of Windows to the processor first. That is now clearly out of the realm of "microcontroller".
HTML files aren't even code at all. They are a description of how to display text and other information. This description is interpreted by software known as a "web browser". That's a large piece of code too. And then, microcontrollers don't come with displays built in. And even then, how do you imagine this is supposed to work across a UART link?
Your overall premises are absurd, and show that you have no idea what a microcontroller is, nor what BAT files and HTML files really are or and how they are processed on large systems. You heard some words and thought they could be magically put together somehow. It is wise to not throw around words you don't understand.
Go learn some basics of what a operating system, interpreter, and web browser are, and how computers work at the hardware level. Or start by trying to blink a LED with a microcontroller.