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Yes, it's the multiple independent time series, but we just compute the lag features, we don't add the one hot encoding. You can achieve that by using the id as a static feature and then using a onehotencoder in your model, e.g.

from sklearn.compose import ColumnTransformer
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import make_pipeline

ohe = ColumnTransformer([('unique_id', OneHotEncoder(sparse_output=False))], remainder='passthrough')
ohe_lr = make_pipeline(ohe, LinearRegression())
fcst = MLForecast(models=ohe_lr, ...)
fcst.fit(..., static_features=['unique_id', ...])

Or if your model supports categorical features (like LightGBM) you can just provide the id as a static feature directly (having the id with a categorical dtype)

Yeah, of course. I have a few thousand series of varying lengths and dynamics at the moment so it's not massive data. I'll have a play and see what sort of improvement I get (if any)