It’s almost certainly going to stay at 11 characters. The individual characters come from a set of 64 possibilities (A-Za-z0-9_-).
64^11 is somewhat more than 2^64. (10 characters would not be enough.) So basically each youtube ID is actually a 64bit number. And I quite doubt they will ever run out of those.
If you want to save space in your database you could theoretically convert the IDs to 64bit numbers then convert them back later. But you would need to know how youtube does the conversion so it’s not practical. (Since 64^11 is more than 2^64 you can’t store all possibilities, so you need to know which ones are impossible and google doesn’t say.)
It takes 66 bits to store all possibilities. So you could actually store a 64bit number plus a 2 bit number and save some space that way. Or more practically store 9 8bit values – you would save only 2 bytes per record though over storing it as text, so it’s probably not worth it.