Vyxal (generating Vyxal), 23 bytes, ~\$10^{303}\$\$10^{305}\$
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Thanks to emanresu A for 2 more orders of magnitude
Simple number compression builtin, then chop off the last char. Generates a Vyxal compressed number in base 255. Exceeds the 128 byte output limit at \$10^{303}\$\$10^{305}\$, but can go up to \$10^{308}\$ if the ceiling is raised to 130 bytes.