спасибо Таня 😊

"Мне жаль, что ..." - the meaning is close to "извините", but different.
"извините" implies that the person feels guilty, that isn't necessarily the case.

Grumbler ...l really appreciate for explaining it in details

Grumbler, maybe you have a point. Мне жаль, что мы не могли встретиться ... would be worded as I wish we could have met under better circumstances. If they are the same, I will admit that you're right.

TBH, I am not sure
According to https://www.thefreedictionary.com/be+sorry, there are 3 meanings:
1. sadness and disappointment
2. apologizing
3. giving bad news

"извините" is (2) or (3), but in the examples I don't see clear difference between (1) and (2)

BTW, another option without apologising - it's a pity

I belive "i'm sorry" could mean both извините and мне жаль. I wouldn't see their meaning as different, anyway I like you option better. ;)