Problem is that there's no guarantee that twitter won't apply lossy transformations to your data (in fact, it's guaranteed that it does). So either you would have to encode the data with lots of redundancy and/or error correction, or you have to encode in like, QR code or something similar, and rely on image recognition to extract it.
Inside the range of characters support by twitter, your data is "guaranteed" to not change
In 2018 people discovered that Twitter would recompress images but leave the embedded ICC profile, if present, intact, and used that to make a Twitter-surviving JPEG+ZIP polyglot[1], although that got patched out once someone used it as a C&C channel[2]. Apparently that still worked (and was utilized for the same purpose) on Steam user profiles in 2021[3].
Or the 1000 characters of the Alt tag. Since you can have multiple images per tweet, your limit just jumped without having to worry about images getting edited.
Inside the range of characters support by twitter, your data is "guaranteed" to not change