If this was done on an online machine, there are inherent risks to it, like malware that somehow pwns the password manager and steals your seed, or a clipboard malware, etc. But since we are talking about cold storage setup, the password manager would just be used as an encryption/decryption tool.
I always read online when it comes to storing your 12 or 24 words, never to store them digitally. I assume this is because most people will put then in an unencrypted file like a TXT or DOCX file and not use a password manager like KeePass.
I was thinking of using Tails OS offline to create a new KeePass file and enter the 24 words in the file, save the file and put it on a USB stick. Turn off the Tails OS. And make copies of the keepass file on top other drives.