The addon really only spoofs the UA to a Chrome one, so Firefox gets the same page that Chrome does. In other words, this should also happen if you likewise change it with another addon.
The issue is likely that Google Search’s Chrome version is now using some code that somehow hangs on Firefox, and I haven’t been able to reproduce the issue to diagnose it, sadly.
The addon really only spoofs the UA to a Chrome one, so Firefox gets the same page that Chrome does. In other words, this should also happen if you likewise change it with another addon.
The issue is likely that Google Search’s Chrome version is now using some code that somehow hangs on Firefox, and I haven’t been able to reproduce the issue to diagnose it, sadly.