Line transversal
A row or column's pairs must form a matching of its letters to its digits; forced completions are sound
How to use it
This is transversal's Line matching pass, the cheapest of the three to try.
Zoom into one line. A row (or column) must contain each letter once and each digit once, so its empty cells are filled by marrying its missing letters to its missing digits — a bijection, with every resulting pair distinct and admissible at its cell. List the ways to complete the marriage; a pair that survives no completion cannot sit in that line, and a cell with a single surviving option is forced.
Lines with two or three empty cells are the readable ones: their matchings fit in the head. The eliminations prune candidates across both layers at once, since a blocked pair kills the letter side and the digit side together.
Why it is sound
A row (or column) of a valid Eulero grid carries each letter once and each digit once, so the pairs in its empty cells must form a matching between the available letters and digits, with every pair distinct (orthogonality). Enumerating the completions of one line is exact and bounded; a pair that survives no completion is impossible, and a cell with a single survivor is forced. Sound because it only removes configurations absent from every solution.