What are the chances of bitcoin going extinct?
Why do you have this mindset. Is it because you don't owe no bitcoin? There could be some bitcoin that might not be accessible due to inaccessibility to private keys, forgotten private keys, see d phrase mismatch and loss of paper wallets but that does not mean bitcoin will go to extinction.
It doesn't even make sense to think this low, it means you have not been paying attention to what has been happening around Bitcoin. Take for for instance today, ETF Bitcoin has cross a milestone of $10b, this means that institutional investors has invest more than $10B within a space of one month after Bitcoin ETF has been approved, we don't know how the numbers will grow in the coming months, you think with such investment coming to Bitcoin, it will die and be forgotten one day? Extinction is not the right word to be used here.
The only challenge here is Bitcoin supply, it will continue to shrink and miners will continue to have less and less number of Bitcoin until 100 years to come. What will happen next depend on what will happen next on price and the next thing to do will happen by then, so for now just focus on the growth because bitcoin is too real to die, you should have asked this question 7 years ago when people were having so much doubt about the future.