Should \(SVD,...) truncate small singular values?

This is a follow up on the discussion in https://github.com/JuliaLang/julia/pull/32126. Currently, `\` and `inv` truncate the smaller singular values, i.e. it actually computes a pseudo-inverse (or applies regularization if that is your preferred language). That is sometimes beneficial and the SVD is used for this purpose but I'm wondering if we should make the truncation/regularization explicit, i.e. let `inv` be the untruncated inverse and use `pinv` for the truncated version. Similarly, we could add a relative tolerance keyword argument to `ldiv!` which would default to zero, which would mean no truncation. The issue is `\` which is an operator so we can't really control the behavior with an extra argument (when used as infix). Thoughts?