I remember having the discussion that Tracks > [X] Update the display while playing only affected playback and not recording. It doesn’t. It affects both. So either the action is wrong or the prompt is wrong.
It affects “transport”. That is, it affects Play, Record, Timeline Quick Play, Scrubbing, Seeking and Play at Speed.
As far as I recall it’s always been like that (though we didn’t have all of those in previous versions). It’s certainly does that in Audacity 2.0.0.
Note that it can now be turned on/off much more conveniently from the right-click Timeline menu: “Do not scroll while playing”.
It’s clearer if you were using 2.1.3-alpha. That has a new button for Pinned/Unpinned Recording/Play head.
When “Pinned”, the recording or play head is centred, and the waveform moves continuously during transport, instead of scrolling only when the head reaches the right edge of the project window.
Pinned record.play head has been a popular feature request for years - I seem to recall from my dim and distant memory, you yourself Koz, asking for just that a while back
Anyway we now have it, thanks to Paul Licameli, for the upcoming 2.1.3 - it started out as a part of new-scrubbing, but was broadened out to affect all transport.