Is the interconnecting cable between outdoor and indoor AC units classed as a control cable or power cable?

I suppose there is rather a precedent for the HVAC industry using SY ... even though many manufacturers labelling it as a control cable (although others have claimed at least part BS compliance).

should comply with BS or harmonised standards

OR ... IEC or the appropriate standard of another country (133.1.1) OR the designer confirms that it provides at least the same degree of safety (133.1.3) - so it's not quite a simple yes/no.

Of course there's nothing stopping a control/auxiliary circuit running at full mains voltage (e.g. see fig 55.1)

   - Andy.

Indeed, plenty of thermostats, fan controllers, lamp dimmers and so on are  a kind of "mains level" logic

Mike.

Indeed, plenty of thermostats, fan controllers, lamp dimmers and so on are  a kind of "mains level" logic

Mike.