When we deal with many different multivariate time series, each time series can have a different number of variates. So "any-variate" means that the model is able to take as inputs multivariate time series with arbitrary number of variates, and model the interactions with the Transformer's attention mechanism. This is something that many other TS foundation models do not consider yet - they convert all multivariate time series into multiple univariate time series.
Whether or not the forecasts improves as a result of the additional covariates is still an open question which needs to be studied more -- we need to build better evaluations and benchmarks for this.