It sounds like the turbo oil seals failed, either as a result of damage to the turbo vanes or bearings, or the seals failed resulting in damaged bearings.
Hence the white smoke -- oil was leaking into the red-hot turbo's exhaust chamber and burning, possibly combined with oil going into the inlet side and being burnt in the engine. The siren noise is also characteristic of dying turbo bearings.
Reconditioning turbos is quite common and a properly recon'd unit will be as good as new. Ask the garage to tell you who is reconditioning it, and look them up on the web.
If the seals failed (and they can do this just through wear & tear) then there shouldn't be any damage to other engine components. I would insist on an oil / filter change, although they are likely to do this anyway, as the turbo has a direct oil feed.
You also did the right thing by stopping the car and waiting for a tow.
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