This is kinda a poll. Please reply, and answer the 2 questions shortly, so I can get a grasp of your feedback.

I want to know if there is a desire for this, or if it already exists. Years ago I started to work on a python program called "spellcheck-dir" It would recursively look at files in a project, and look at their output. Regardless of if the output was a web browser, or a command line program. I'm not talking about checking the spelling of variables, functions, and class names. I am talking about the actual text that the code would output to an end user. To do this, I had to write multiple lexical parsers, one for HTML, JavaScript, Python, PHP, etc. I hadn't finished this tool. Now I am interested in finishing it, but it has been 10 years.
In case there is any confusion, let me give an example. You just finished a PHP site for a client. You are about to push it live. The entire site lives in some public_html directory. The command you would run would be "spellcheck-dir /home/client-dev-staging/public_html" It would then sit and run interactively finding words that were spelled wrong, and asking the user if they wanted to replace with suggestions, edit manually, ignore, ignore always, etc. After I finish this, I would put it on github so that other programmers could add in parsers to handle more and more file types.

2 questions for you, #1, does something like this already exist? And #2, if not, is there a desire for this? Is this something other programmers would use?

Side Note: I had someone message me, stating that you would need to execute the code, running all possible outcomes. That isn't necessarily true. Simply a lexical parser (though a complex one) should do the trick, for 99% of all text generated via code. It actually is quite simple in concept. The only words that would get skipped over without executing code would be ones that are actually generated on the fly. But that rarely actually happens in code. Even in cases of tense, singular or plural, you still generally have the root of the word typed. This tool would at the least capture and check that word.

The only words that would get skipped over without executing code would be ones that are actually generated on the fly. But that rarely actually happens in code.

Hah! Tell that to front end developers.

I am a front end developer. IDK, I know I would persoanlly like this tool, but why spend a few days finishing it if something out there already exists. Even each time I add a new module to an existing project, it would be nice to be able to spellcheck it before deploying it.

1 Don't know if it exists.
2 Not to me, if you use a decent IDE it has spellchecking already built in. If you don't, most likely you use string resources and templates which would contain all user output. These are more easily checked than code.

spell checkers in IDEs are pretty much useless unless you're creating an application with a user interface that's displayed in American English without specialist words and phrases.
And of course it's not just spelling that can go wrong, but grammar as well. And there you're in even bigger trouble as there are many things that are technically incorrect but so ingrained in the verbiage of professional audiences you are probably targeting your system at that "correcting" them would cause a lot of confusion.

And of course quite often a user interface will have to use shorthand for longer terms, shorthand which may not be known to a generic lexicon and certainly isn't grammatically correct.