There is some doubt about the wikipedia entry. The source it cites for the depth charge claim is here. This is the relevant section:

10-27 April 1944:

Dry-docked in Kure drydock No. 4, where repairs are made to the hull. The 15.5-cm wing turrets Nos. 2 and 3 are replaced by three triple 25-mm unshielded AA mounts on each side. Sixteen 25-mm triple mounts and 25 single mounts are added, increasing the number of their directors to fourteen. Two 150-cm searchlights (Nos. 7 and 8) and their directors are removed to make room for new 25-mm mounts and their directors. The searchlights are later reinstalled for use by Sasebo's AA batteries. MUSASHI's resulting AA suite is one hundred and fifteen 25-mm AA guns (30x3, 25x1). Two Type 22 surface-search and two Type 13 air-search radars are installed.

There is no mention of depth charge rails on the ship itself, only depth bombs being used by the ships aircraft (See the 28th of March 1944 entry). Edit: Looking at the wayback machine, the mention of depth charge rails on the page was removed in November 2013. The data from that page looks like it's been copied directly into other books on the subject before the page was updated - e.g. History of Japanese Capital Ships 1868 to 1945 by Hans Lengerer or The Japanese Navy in the Pacific War by Mark Stille

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Looking at Anatomy of the Ship: Battleships Yamato and Musashi by Janusz Skulski and Stefan Draminski (Conway Publishing, 2017), the fantails after the 1944 show Yamato with platforms for 2 triple 25mm cannon and 2 single 25mm cannon and Musashi with 4 single 25mm cannon with 2x2 depth charge racks either side of the stern-most pair of cannon. 4 depth charges wouldn't have been very effective (Allied escorts in the Atlantic were using depth charge patterns with 10+ charge). The book notes regarding sonar on the battleships:

Both battleships were equipped with Type '0' sonar arrays that could detect a submarine when the ship was dead in the water or moving at slow speed.

Bismarck was also reported by survivors to have carried depth charges (see here under 26th of Mary 1941 and Anatomy of the Ship: The Battleship Bismarck by Stefan Draminski pp 23 - they were blown off by the main guns firing)

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The only battleship known to have sunk a submarine was HMS Dreadnought, who rammed and sank U-29 on the 18th of March 1915 (Wikipedia notes that USS New York may have collided with and sunk a submerged submarine in 1918, but there is no conclusive evidence).