In the field of cryptography, which relevant to your context of passwords, plaintext (noun) is a technical term referring to the message that has not been encrypted. It is contrasted with ciphertext, which refers to the encrypted message. The separated form plain text is somewhat different and does not relate specifically to cryptography, so will be ignored in this answer.
Both forms in/as plaintext are grammatical, but mean different things. Storing the password as plaintext means that the password is stored without encryption. Storing the password in plaintext can have the same meaning, but it can also be read as an attempt at steganography, or hiding things in plain sight (for example, by inserting the password as an extra word in a given sentence).
With the addition of the word form, the word in now applies to form rather than plaintext, so in plaintext form carries the same meaning as as plaintext, as you suggest.
You asked in comments about a 10:1 ratio in favour of in plaintext. Since in plaintext includes and goes beyond the semantic range of as plaintext, this is perhaps not as surprising as it might first seem. Also, stored in plaintext parallels common phrases such as stored in lists (or other data structures) and stored in the cookie jar, and in plaintext sounds identical to the separated form in plain text, which parallels the common expression in plain sight. All these are plausible reasons for authors to think of the in form when writing. We're now crossing heavily into psychology, so I'll leave it at that.
TL;DR In answer to your question, as plaintext expresses your intent better than in plaintext.
