This question resembles recursion, because your interpretation is 惜しい.
I would translate the bold part sentence literally as "Since this time it is regrettable that your answer is wrong, I would take it as a safe".
Yes, your word-to-word literal translation per se, is not wrong. I'll elaborate on the "regrettable" and "safe" later.
I can’t tell it from its literal meaning. I guess it’s because I don’t understand the word セーフ.
I disagree. I think the primary reason is, because you don't understand the nuance of 惜しい.
And if the sentence implies "but", why is ので used? Shouldn’t it be のに?
寿季's mindset: You're wrong, but it was almost correct. ので (Therefore) I will give you a free pass this time.
Your mindset: You were almost correct, but you're wrong. のに (But) I will give you a free pass this time.
のに is not the best choice here, but I tried to stick to your choice of words.
I guess it’s because I don’t understand the word セーフ.
Let's use baseball as an example here. If the batter makes it to the base before getting tagged, the batter is safe. If too late, out.
If you're from a cricket region, replace safe with in and out remains out. Again the batsman must make it across the line before the ball hits the wickets.
The umpire (寿季) is saying, "well, you were technically out, but it was close enough, therefore I will consider this safe/in".
Now let's dig into 惜しい. Practically, we use the word to express "that was close". If someone answers almost correctly, you can just say "惜しい" and they'll understand that the answer was not too far off.