- I'm very sorry that I can't join you.
- I'm so sorry that I can't join you.
Which one is grammatical and correct? Thanks in advance.
I don't think either is incorrect, or that the "that-clause" has any special rule for using "so" vs. "that".
I'd say "so sorry" sounds emphatic/emotional. "very sorry" sounds more plain and formal, but maybe more sincere.
Althought the "so" version can be more emotional, in certain contexts it can add a tone of sarcasm, especially if you're appologizing for something minor. I'd avoid this expression unless you think you can convey your tone unambiguously.
I think the most idiomatic expression in American English is "really sorry", but that is casual.
In a more formal situation I'd use no adverb at all, and in very formal situations use "apologize".