better... 1/ Sorry for not responding, I've been really busy lately/ recently 2/ Sorry for taking so long to respond, I've had a lot on my plate recently.

For the first sentence, a native speaker would probably say " I've been really busy lately" instead of "so far" . Even though "so far" can be sort of translated into "up to now" it doesn't really work well in this sentence. The second sentence is all good!

1/ Sorry for not responding, I've been really busy so far TODAY. 2/ Sorry for taking so long to respond, there's been a lot on my plate recently