Okay, say you have an input of (1000 instances and 30 features). What I would do based on what you told us is:
Train an autoencoder, a neural network that compresses the input and then decompresses it, which has as a target your original input. The compressed representation lies in the latent space and encapsulates information about the input which is not directly accessible by humans. Now you may find such networks in tensorflow or pytorch. Tensorflow is easier and more straightforward so it could be better for you. I will provide this link (https://keras.io/examples/generative/vae/) for a variational autoencoder that may do the job for you. This has Conv2D layers so it performs really well for image data, but you can play around with the architecture. I cannot tell u more because you did not provide more info for your dataset. However, the important thing is the following:
After your autoencoder is trained properly and you need to make sure of it, (it adequately reconstructs the input) then you need to extract the aforementioned latent inputs (you will find more in the link). Now, that will be let's say 16 numbers but you can play with it. These 16 numbers were built to preserve info regarding your input. You said you wanted to combine these numbers with your input so might as well do that and end up with 46 input features. Now the feature selection part has to do with selecting the input features that are more useful for your model. That is not very interesting, you may find more information (https://towardsdatascience.com/feature-selection-techniques-in-machine-learning-with-python-f24e7da3f36e) and one way to select features is by training many models with different feature subsets. Remember, techniques such as PCA are for feature extraction not selection. I cannot provide any demo that does the whole thing but there are sources that can help. Remember, your autoencoder is supposed to return 16 numbers for each training example. Your autoencoder is trained only on your train data, with your train data as targets.