Thus, an attacker, having access to one part of your backup, will be able to assess his prospects. In this case, he will need to gain access to only one more part of the backup.
Getting that info isn't too helpful to an attacker in most scenarios if you stored your backup in separate locations.
Even though the attacker knows how many more backups are there, it's useless without a clue to where to find it.
You may be thinking of a $5 wrench attack where the attacker could torture the owner to tell the whereabouts of the other parts.
So should you switch to the new 20-word backup or continue to use the familiar 12 or 24 words?
If you can, use multiple.
At least compared to a single backup, your bitcoins can still be safe in case one of the backup is compromised.