Some intrinsic implementations of tanh have low precision. This is found across nvidia directx (4070). It may be across all nvidia. This can easily be seen by running the CTS for tanh on device and is limited to f32.
https://gpuweb.github.io/cts/standalone/?q=webgpu:shader,execution,expression,call,builtin,atanh:*

A polyfill with sinh/cosh appears to be at least 2x slower (on said device).

Based on the data I am suggesting a 1e-5 absolute error be added as acceptable range.