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I%5Œg%8ċ1ドルṀμÐṀḢ

A monadic link taking a list of lists of digits, and returning the leftmost one containing a maximal run as described.

Try it online! or see a test suite (with processing to make I/O look like it is in the question).

How?

I%5Œg%8ċ1ドルṀμÐṀḢ - Link: list of lists of integers (digits) from [0-9]
 μÐṀ - keep elements for which the link to the left is maximal:
I - incremental differences (i.e. [a2-a1, a3-a2, ...])
 5 - literal 10
 % - modulo by (i.e. [(a2-a1)%10, (a3-a2)%10, ...])
 - this equates deltas of -9 and -1 with 1 and 9 respectively
 Œg - group runs of equal elements
 %8 - modulo by 8; vectorised (9s become 1s, others unaffected)
 ċ1ドル - count number of 1s in €ach group
 Ṁ - maximum
 Ḣ - head (get the first one of those that were maximal)