Good question! I would say no- we don’t use dates in that way with the present perfect. Your second option is the most accurate one here.

I'm glad you asked this question. The present perfect tense (such as "I have filed") is not a past tense. It is a present tense. It makes a statement about the present moment. It does not talk about a past moment. When you say "I have filed" it means that right now at this moment you have, as an experience, the filing of document A. It is an experience that you NOW have. It is a statement about something YOU currently have done. If you want to tell a client that you DID something, you should use the past tense: "I filed document A today". It is not wrong to say "I have filed document A today" and in some situations it would be the best thing to say. However, if you are talking to a client about something you did for his benefit, it does not sound as good because you are talking about yourself, about your own personal experience, rather than talking about what you did. If you changed the wording somewhat, the present perfect would sound good: "Dear Client: I am pleased to inform you that as of today, September 28, I have filed document A." and that sounds good because it says that you are happy that you have accomplished something for the client.

If you want to be extra thorough, I would often say: 'I have filed document A today, Sept. 28th.' Or you could place the date in parenthesis. Or 'Document A has been filed with a filing date of September 28th.' Including the actual date can be helpful, especially across different timezones, etc.