Update DeepSpeed precision handling after moving PrecisionPlugin

[awaelchli]

What does this PR do?

Part of #10416

Now that the PrecisionPlugin has been moved into the strategy / training type plugin, some logic around setting precision variables within Lite is no longer needed. In addition, access to precision related settings within the DeepSpeed plugin can be simplified.

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Did you have fun?

I made sure I had fun coding 🙃

Part of #1 (it's a lie, this is just here to avoid noisy GitHub bot)

cc @Borda @justusschock @awaelchli @akihironitta @SeanNaren

[four4fish]

Awesome!! 👍

[SeanNaren]

So glad we've finally cleaned this up, thanks @awaelchli :)

[tchaton]

LGTM !