Testet using only Accessories 1.5.3 and Library 7.0.8 on Forge 1.20.1.
The Certificate of Taming appears to increases the stats of the tamed entity, but after Exiting and Re-Joining the world, the stats revert back to normal.
This happens both on a Server and in Singleplayer.
I have tested it with taming Wolf and Horses.