the following site might help you:

https://artemiorimando.com/category/uncategorized/

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WoE does not do variable selection at all, so it is indeed different from lasso !

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the only positive point to WoE recoding i know of is to possibly simplify the regression analysis for continuous variables with non monotonic influence on the target : an astute binning of such a variable will make the influence monotonic across bins and therefore you do not need to add polynomial terms to your regression

BUT

the binning process itself is prone to errors and overfitting

(a similar argument and pitfall applies to binning together modalities of a categorical variable with many modalities)

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to use WoE encoding on many variables, you need a robust supervised binning technique (if you have indeed many variables, you won't do the binnings manually), something like MDLPC for continuous variables

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you'll end up with encoded variables and then apply lasso which will perform variable selection

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