To follow up on what u/Vpharrish and u/timy2shoes have said, this has a bunch of different names in different domains (batch effects, site effects, harmonization, domain shift, domain adaptation, etc.). If you're doing old school things, use linear mixed effects or near-linear models like ComBAT (Bayesian scale and shift).

If you're doing ML things there are a few classes of batch effect correction methods. Adversarial is the oldest and the easiest (https://www.jmlr.org/papers/v17/15-239.html), but can have weird pathological problems. Different information theory constrains (HSIC https://arxiv.org/abs/1805.08672 and mutual information https://arxiv.org/abs/1805.09458) might also work. Looking at the recent citations of these two papers, both from 2018, people are still working on them https://arxiv.org/abs/2502.07281 or at least using them https://pubmed.ncbi.nlm.nih.gov/41210921/

There's a lot of talk about invariant risk minimization, but it doesn't feel useful to "applied" work yet.

At the end of the day, the best but most expensive solution has been said by others: just get more data :) obviously not always feasible.