SMOTE oversampling for class imbalanced dataset introduces bias in final distribution
Class imbalance is a frequent problem in machine learning and techniques to balance the data usualy are of two flavors: undersampling the majority, oversampling the minority or both.
One can always partition the data according to some variables and separately oversample each partition so as to maintain some measure (eg given data distribution). In the same way that separate oversampling can be achieved for only $1$ variable, in the same way separate oversampling can be achieved for $n$ variables. Of course more complex but certainly doable. For example one takes all distinct combinations of variables (or ranges of variables for continous variables) and separately oversamples each such cluster in order to maintain the given data distribution.
The above is a straightforward technique, although one should note that if minority class does not have enough samples there is no guaranty that the given data distribution reflects the (true) underlying data distribution (in other words it may not constitute a representative sample in statistical sense). So for these cases oversampling the whole data, without extra assumptions about underlying distribution, is a maximally unbiased method in the statistical sense.
There is some research lately on hybrid and intelligent methods for (oversampling) class imbalance problems without introducing bias during the process. The following references will provide the relevant background:
Cross-Validation for Imbalanced Datasets: Avoiding Overoptimistic and Overfitting Approaches, October 2018

Although cross-validation is a standard procedure for performance
evaluation, its joint application with oversampling remains an open
question for researchers farther from the imbalanced data topic. A
frequent experimental flaw is the application of oversampling
algorithms to the entire dataset, resulting in biased models and
overly-optimistic estimates. We emphasize and distinguish overoptimism
from overfitting, showing that the former is associated with the
cross-validation procedure, while the latter is influenced by the
chosen oversampling algorithm. Furthermore, we perform a thorough
empirical comparison of well-established oversampling algorithms,
supported by a data complexity analysis. The best oversampling
techniques seem to possess three key characteristics: use of cleaning
procedures, cluster-based example synthetization and adaptive
weighting of minority examples, where Synthetic Minority Oversampling
Technique coupled with Tomek Links and Majority Weighted Minority
Oversampling Technique stand out, being capable of increasing the
discriminative power of data

Learning from Imbalanced Data, 9,  SEPTEMBER 2009

With the continuous expansion of data availability in many
large-scale, complex, and networked systems, such as surveillance,
security, Internet, and finance, it becomes critical to advance the
fundamental understanding of knowledge discovery and analysis from raw
data to support decision-making processes. Although existing knowledge
discovery and data engineering techniques have shown great success in
many real-world applications, the problem of learning from imbalanced
data (the imbalanced learning problem) is a relatively new challenge
that has attracted growing attention from both academia and industry.
The imbalanced learning problem is concerned with the performance of
learning algorithms in the presence of under represented data and
severe class distribution skews. Due to the inherent complex
characteristics of imbalanced data sets, learning from such data
requires new understandings, principles, algorithms, and tools to
transform vast amounts of raw data efficiently into information and
knowledge representation. In this paper, we provide a comprehensive
review of the development of research in learning from imbalanced
data. Our focus is to provide a critical review of the nature of the
problem, the state-of-the-art technologies, and the current
assessment metrics used to evaluate learning performance under the
imbalanced learning scenario. Furthermore, in order to stimulate
future research in this field, we also highlight the major
opportunities and challenges, as well as potential important research
directions for learning from imbalanced data.

Data Sampling Methods to Deal With the Big Data Multi-Class Imbalance Problem, 14 February 2020

The class imbalance problem has been a hot topic in the machine
learning community in recent years. Nowadays, in the time of big data
and deep learning, this problem remains in force. Much work has been
performed to deal to the class imbalance problem, the random sampling
methods (over and under sampling) being the most widely employed
approaches. Moreover, sophisticated sampling methods have been
developed, including the Synthetic Minority Over-sampling Technique
(SMOTE), and also they have been combined with cleaning techniques
such as Editing Nearest Neighbor or Tomek’s Links (SMOTE+ENN and
SMOTE+TL, respectively). In the big data context, it is noticeable
that the class imbalance problem has been addressed by adaptation of
traditional techniques, relatively ignoring intelligent approaches.
Thus, the capabilities and possibilities of heuristic sampling methods
on deep learning neural networks in big data domain are analyzed in
this work, and the cleaning strategies are particularly analyzed. This
study is developed on big data, multi-class imbalanced datasets
obtained from hyper-spectral remote sensing images. The effectiveness
of a hybrid approach on these datasets is analyzed, in which the
dataset is cleaned by SMOTE followed by the training of an Artificial
Neural Network (ANN) with those data, while the neural network output
noise is processed with ENN to eliminate output noise; after that, the
ANN is trained again with the resultant dataset. Obtained results
suggest that best classification outcome is achieved when the cleaning
strategies are applied on an ANN output instead of input feature space
only. Consequently, the need to consider the classifier’s nature when
the classical class imbalance approaches are adapted in deep learning
and big data scenarios is clear.

Hope these notes help.