The reason it's not a mistake in grammar usage is because the author used the word "I've" at the beginning of the tweet. "I've come down with covid but am feeling fine" is correct. "I've come down with covid but I am feeling fine" is also acceptable although the second "I" is not necessary because the "I've" at the beginning of the sentence has the object of the sentence covered.

All that to say, I agree that the same person wrote both texts.