In MySQL. Not setting any speed records, and some of this syntax is deprecated.

day12.sql

DROP TABLE IF EXISTS day12, graph;
SET NAMES binary;

CREATE TABLE day12 (
    rowNum int DEFAULT 1, 
    colNum int auto_increment, 
    cell char(1), 
    primary key (rowNum, colNum)
) DEFAULT CHARSET=binary ENGINE=MyISAM;

CREATE TRIGGER day12_ai BEFORE INSERT ON day12 FOR EACH ROW SET 
    @row := @row + (NEW.cell = '\n'), 
    -- Deliberately violating primary key so that '\n' will be discarded
    NEW.rowNum = IF(NEW.cell = '\n', 1, NEW.rowNum), 
    NEW.colNum = IF(new.cell = '\n', 1, NEW.colNum)
;

SET @row := 1;
LOAD DATA INFILE 
-- 'c:/programdata/mysql/mysql server 8.0/uploads/day12example.txt' 
'c:/programdata/mysql/mysql server 8.0/uploads/day12.txt' 
IGNORE INTO TABLE day12 FIELDS TERMINATED BY '' LINES TERMINATED BY '' (cell) SET rownum = @row;

CREATE TABLE graph (index(rowNum, colNum), index(neighborRow, neighborCol)) AS
    SELECT parent.*, neighbor.rowNum AS neighborRow, neighbor.colNum AS neighborCol, neighbor.cell AS neighborCell
    FROM day12 AS parent 
    JOIN day12 AS neighbor ON (neighbor.rowNum, neighbor.colNum) IN ( 
        (parent.rowNum+1, parent.colNum), 
        (parent.rowNum - 1, parent.colNum), 
        (parent.rowNum, parent.colNum + 1), 
        (parent.rowNum, parent.colNum - 1)
    ) 
    AND ORD(ELT(FIELD(parent.cell, 'S', 'E', parent.cell), 'a', 'z', parent.cell)) + 1 
        >= ORD(ELT(FIELD(neighbor.cell, 'S', 'E', neighbor.cell), 'a', 'z', neighbor.cell))
;

-- UNION DISTINCT would prevent the use of having to keep my own @visited set and use FIND_IN_SET,
-- but only if depth is not included in the select list, and then I wouldn't know what the depth is
WITH RECURSIVE cte AS (
    SELECT *, 
    @found := FALSE AS found, 
    CAST(@visited := CONCAT(rowNum,':',colNum,',',neighborRow,':',neighborCol) AS char(32767)), 
    1 AS depth
    FROM graph 
    WHERE cell = 'S' 
        OR cell = 'a' -- for part 2

    UNION ALL

    SELECT graph.*, 
    @found := @found OR graph.neighborCell = 'E', 
    @visited := CONCAT(@visited, ',', graph.neighborRow, ':', graph.neighborCol),
    depth + 1
    FROM cte 
    JOIN graph ON 
        cte.neighborRow = graph.rowNum AND cte.neighborCol = graph.colNum 
        AND NOT FIND_IN_SET(CONCAT(graph.neighborRow, ':', graph.neighborCol), @visited)
    WHERE NOT @found
)
SELECT depth FROM cte WHERE neighborCell = 'E';