Do my clients need an account?

No. Everything a client does happens on a link: playing the audio, leaving notes on the waveform, replying to yours, and approving. There is nothing to create and no account to remember, on any plan, including the free one.

This is deliberate, not unfinished. An account is a favour you are asking of someone who is paying you, and the usual answer is that they reply to your email instead, which puts the feedback back where it cannot be pinned to a timestamp. The one thing a client is asked for is a name when they approve, because an approval with nobody's name on it is not a record.

If you want the link itself protected, see password-protecting a link.