First and foremost, whenever you encounter a situation like this that sounds like it's going to delete or damage all your files, it's a good idea to backup your files, create copies of it [how?], so that if something bad happens you don't lose all your work.
Now to answer the main question of this article: simply changing the file extension of a file will NOT damage the file, HOWEVER, there is a good reason Windows warns you about this, since there are ways to make your file effectively unusable if you do certain things wrong. Let's understand what they are, so it doesn't happen to us.
Forgetting the Original File Extension
If you just change the file extension of the file, the only thing that happens is that Windows will think the file's file type has changed, since it uses the file extension to determine the file type.
To Windows, any file with a .png extension is an image in PNG format. It will try to generate a thumbnail of any file that has a .png extension because it reasonably assumes that's going to be a PNG image. After all, why would it have the wrong extension? If the thumbnail generator fails, it just doesn't show a thumbnail and I guess the common phrase for this situation would be assumes the image is "corrupted," but doesn't do anything with the file or its data at all.
This means that if you change the file extension of a file, and then change it back to what it was before, the file will be back to normal.
So long as you can do this and the file data hasn't been changed, there is no way for the file to have become "unusable." However, there is a little problem. You have to remember what the file extension was to change it back.
Normally, you don't really need to deal with file extensions, so most users simply don't have memorized the file extension of every file type they use, and in some cases they may not even be able to figure out by themselves what the file extension of a file was, whether by using Google or by trying to create a new file of the same type just to check what extension it is.
If this happens, the file is effectively unusable for that user, because they can't use it anymore, they can't fix it, so it's not a lie. It's a bit dramatic, but it's a fair warning.
Tip: if you changed the file extension by accident and you forgot what it was before, you may be able to undo it by pressing Ctrl+Z inside the File Explorer. This will undo the last operation, which includes renaming, moving, or deleting files.
Overwriting File Loaded Wrong
There is a scenario where you can actually corrupt the file and then changing the file extension back won't help you and the file is really unusable for good: if you open the file in a program that doesn't actually support its type, then save it, overwriting the data with that program's interpretation of what the file's contents are supposed to be.
For the record, you don't actually need to change the file extension to do this with some programs, but changing the file extension changes what application is associated with opening it, which makes it easier to accidentally corrupt the file.
A good example of this is Notepad. Text editors are often able to open ANY file because the plain text format is extremely simple.
In plain text, when the character encoding is ASCII (ANSI), each byte represents one character of text. Ideally, this means that a file with 500 bytes would display 500 characters if you open it in Notepad, even if it's an image file. However, there is one problem: some characters are invisible.
And I'm not talking about whitespace characters, I'm talking about characters in ASCII that are meant to represent keys of the keyboard, and haven't been really used for anything in decades. For example, there is a character for the delete key that is supposed to represent pressing the delete key.
If Notepad supports this, that means whatever character comes after this character is going to be deleted the instant the file is loaded. If Notepad doesn't support this, that means that character won't be preserved inside Notepad after the file is loaded.
In both cases, the data inside the file won't match the data that inside Notepad after the file loading process is completed. And this is for ASCII. Nowadays text is encoded using UTF-8, which has countless other ways to have an invalid sequence of bytes that can't be converted to text and then back to same bytes.
This means that if we opened an image file in Notepad, there is a good chance the data it will show as plain text won't perfectly match the actual bytes of the image file, since some bytes simply aren't associated with text characters at all. If we tried to save the file after opening it, it would overwrite the file's data with Notepad's interpretation of the valid characters it found on the file, which essentially means some bytes would be removed completely from the image file.
After doing this, if we changed the file extension back and tried to use it as an image again, the image probably would be broken, and wouldn't load anymore. In other words, it would have become unusable, just as Windows warned us it would happen.
The same thing can happen if we somehow manage to open a text file in an image editor. It will interpret the bytes as if they were of an image, perhaps working around sequences that seemed invalid, and when you try to save it, it will save its valid interpretation of the bytes instead of the bytes that don't form a valid image that you had in the file.
Conclusion
The warning Windows gives makes sense, but it's nothing to worry about once you know what the risks are, specially if you have a copy of the file in case things take an unexpected turn or you end up accidentally saving the file you opened when you didn't mean to (or the program did it automatically for you).
Besides creating a copy, you can also go to the file's properties and change it to "read only" so that it can't be overwritten by accident.