I'm pretty sure the author is mistaken. Separate wallets help with other attacks (i.e. Janus), so you might still want to do this anyway, but I don't think it's relevant for this attack.

There is no difference seen on-chain from you sending your entire balance to a 2nd wallet VS sending your entire balance to the same wallet.

You would still have the same number of inputs/outputs and you would generate a completely new stealth address in either case.

Unless I missed something, and if so lmk, but I can't see any difference.

I know they warn about churning, but I'm not suggesting to continuously do this, just as a thing you do once in awhile, or as often as you would do if you followed their advice with a 2nd wallet.