TLDR You could use an LLM to help you but don't rely on it to do the whole thing correctly for you in a single prompt (request).
I would find it unlikely for an LLM (like ChatGPT or LLaMA) to produce systematic factual information like that either now or in the future. There might eventually be processes that use an LLM as one component that could do it.
The reasoning here is that an LLM gets a statistical picture of all its training data (books and websites and such) - they do not operate on facts or abstractions of patterns by meaning. They tend to reproduce text that looks factual or like an abstraction because the most statistically likely patterns will involve the words that come in a sequence that happen to be facts (or abstractions).
For example, 'This banana is ...' and 'Cars are a kind of ...' will usually get 'yellow' or 'vehicle' respectively to follow, not because those exact sentences have been seen in the training corpus before, but because those words and nearby words with similar cooccurrences are more likely. Another way of saying this is that LLMs are in some sense hallucinating -all- the time, we just don't notice when reading outputs unless the random sequence is wrong factually.
It could be that someone on the internet has created exactly such a table, or at least parts of it. LLMs are not web searches (the training corpus is a fixed subset of the internet - it's not up to date and it is not all of the internet (which is not even all of human knowledge). But an LLM can sort of extract a lot of patterns out of that data that is sort of like Wikipedia.
That said, an LLM can probably get you a lot of that work for you. It may not be complete, it may have a few errors, and it may give you more than is intellectually supportable. If you already know a lot about the subject that's in your table, then I think an LLM would be a good tool for you to help you start off and compile examples and to format the table. But you should use your expertise to manage all that.
If you're not an expert in the subject, then don't rely on anything that is factual. It can give you a good rough idea but any individual 'fact' should not be relied on. (kind of just like wikipedia).
I'd suggest using an LLM incrementally but also to revise and go back a step.
For your exact subject matter, you probably want to ask first what the main categories of verb forms are explicitly saying 'For example: aspect, mood, tense, ...' Or 'statement, question, negation...', things you already know to be the case. Then refine and ask about the different tenses, the different moods, etc.
At some point you can then prompt your LLM to 'combine all these into one table...'. It will most likely not be exactly what you want but then you can repeat pieces of this process to improve it little by little.
I think you'd be able to produce a table that is good enough for you, but I'm not sure it would be of a quality that would be universally acceptable.
(you definitely can do this same process for other languages, but you probably want to do it -in- that other language and have different categories as starters)