I think we are actually talking about a standard error of a parameter estimate here, not a standard deviation. You first should think about conceptually what you are actually trying to estimate here, as the docs of LsqFit say there are some assumptions being made
Assume the errors in each sample are independent, normal distributed with zero mean and same variance, i.e. ϵ∼N(0,σ2I)
which might or might not make sense (especially homoskedasticity is often a problematic assumption on real world data at least in the social sciences, I’m not a kite power plant modelling expert so YMMV).
But indeed your model is linear so you can just estimate it with GLM or FixedEffectModels and get heteroskedasiticty-robust standard errors as well if that matters to you.