Alter column fails due to "hidden" statistic
After reaching out to Azure support, I have managed to solve the issue.
Part of the support engineer's answer included the following:

I've reviewed internal telemetry and can confirm that the statistic listed in the error does not exist. This is likely a compute-node-level statistic that wasn't cleaned up properly.

I was able to confirm and fix this issue by doing the following steps:

Run a CTAS to create a copy of the table
Rename the previous table to something different (eg: ) and the new one to the original table name
DROP the old table

After that, the ALTER TABLE statement worked as expected.