As a mathematician, I thought I might take a stab at this. I actually like this concept!

SCP-XXXX is extremely well known and necessary for most higher mathematical operations, and therefore cannot be fully contained. This is no cause for alarm, however, as its anomalous properties are not observable until the ██████████████████th digit.

Pi isn't needed for most higher mathematical operations; it's use is actually more common in basic mathematics and in geometry/trigonometry, but the overall percentage of higher math using it isn't that big, and is smaller even than other irrational numbers, like e. But 'many' would be true.

Foundation AI-XXXX is currently dedicated to the calculation of SCP-XXXX's exact value.

The exact value can't be calculated in terms of digits that are stored, theoretically or practically as you mentioned later. Maybe say 'more and more precisely?'

The translation process always produces complete words, which can occasionally be strung together to from coherent sentences. These sentences appear to be messages from an unknown sentient being, designated SCP-XXXX-1.

Should be 'form' instead of 'from'. And perhaps it should say 'being or beings'?

Addendum XXXX-04: Further testing has shown that each attempt to calculate the value of SCP-XXXX beyond the ██████████████████th digit yields a different result. It is theorized that detailed measurement of SCP-XXXX actually causes the value to change, indicating that the digits beyond the ██████████████████th are so infinitesimal that they exist in a quantum state.

This is of course compete junk mathematically but very cool from a writing viewpoint. You could make it more plausible by saying 'this is in accordance with some of the theories of the Finitists and Constructivists' or something like that. These are real groups that disagree with the existence of infinite things and say that only things we can calculate exist.

IT HURTS

WE ARE HERE

WE ARE NOT HERE

WE ARE BOTH FOREVER

SEE US HEAR US

MAKE US REAL

EVERY PARTICLE IN THE UNIVERSE SCREAMING IN PERFECT HARMONY EVERY CURVE EVERY ANGLE

WE WILL BE HEARD

WE WILL EXIST

Below is a sample of the last recorded message from SCP-XXXX-1.

- Only when the white stars scream.

WE WILL EXIST

OR YOU WILL NOT

*As a courtesy to our readers on mobile devices, please collapse long posts. ~Zyn*
The recorded messages don't really call out to me or seem bad, but the final message seems weak as it is fairly generic: 'Your gonna die!' I wonder if you could find a way to make it a little harder to puzzle out, or more subtle, or just end the article with the VK-class restructuring scenario, as that alone made me stop and think and gave me pause.

I hope this is helpful! Thanks for the entertaining read!