Is it possible to unscramble a scrambled ed25519 SSH key? Let's say I generate an ed25519 SSH key with ssh-keygen -t ed25519. Then I take the private key file and randomly scramble the order of base64 encoded characters. Is it practically feasible to recover the original key from this scrambled file?
Is it possible to unscramble a scrambled ed25519 ssh key?

I think you confuse the encryption with the scrambling. Scambling doesn't require a key and it may require a large amount of memory even for the owner to unscramble it if it is a true permutation. Yes, scrambling is a permutation.
Assume that there are $n$ elements that you want to scramble then there are $n!$ permutation if we consider they are all distinct. To store the permutation one needs $n! \times n \times x$ bits where $x$ is the number of bits to represents the elements. For generic cases the repeating is not necessary, so live with this huge number.
We can find the number of base64 characters for $m$ bits with the formula $\lceil(m / 3) \cdot 4 \rceil$. Place the length of the PEM file or just the private key 256 bits that is 32-byte then we have $\lceil 128/3 \rceil = 43$ base64 character for the private key. That will require $43! \times 43 \times 64$ bit to store. This makes approximately $2^{186.7}$ bits, impossible!
This is why we use block ciphers to encrypt and we call a block cipher a family of permutations. Those are expected to select a random permutation from all possible permutations with a key. Even the total number of the permutations of a 128-bit block cipher is tiny compared to all possible permutations $(2^{128})!$. We can see this with the help of Stirling's formula
$$2^{b}! \approx \sqrt{2\pi 2^{b}} \bigl(2^{b}/e\bigr)^{2^{b}}.$$
$$2^{128}! \approx \sqrt{2\pi 2^{128}} \bigl(2^{128}/e\bigr)^{2^{128}} \!=  \sqrt{2\pi 2^{128}} e^{-2^{128}} \bigl(2^{128}\bigr)^{2^{128}} \ggg 2^{128}$$
So, as long as you are not playing a game with a friend ( like CTFs), then secure scrambling has no practicality.

Then i take the private key file and randomly scramble the order of base64 encoded characters. Is it practically feasible to recover the original key from this scrambled file?

The source you linked is using a passphrase for the encryption of the contents of the PEM file - that is not scrambling -. This passphrase is hashed with SHA-1 (old version uses MD5) to derive a key and then the contents of the PEM file is encrypted with AES-128 in CBC mode with this key.
AES-CBC is CPA secure and to break it you need to search $2^{127}$ keys on average.
The common attack is not the key, the user's bad passwords. John the Ripper password cracker and the hashcat are ways to break it. There are currently  613M pwned passwords to easily test! They are already in SHA-1 format as ssh uses SHA-1 to derive the key.
The usual advice to mitigate this is using the diceware based passwords to have passwords with good strength. Or, see XKCD 936.