Update FSDPPrecision to support 16-true precision setting

[awaelchli]

Description & Motivation

We recently added true precision support in Fabric:
#17287
#17576

The FSDPPrecision plugin needs an update to support the strings "16-true" and "bf16-true".

Pitch

Update the plugin's code by following the same pattern as in #17576.

Alternatives

No response

Additional context

No response

cc @Borda @justusschock @awaelchli @carmocca

[carmocca]

I think #17670 fixes this issue too

[speediedan]

You guys may have observed this internally already but if not I thought I'd share that though #17670 partially addresses this issue, patching of at least the following two sections was required to enable FSDP 16-true support for the downstream package I maintain: https://github.com/Lightning-AI/lightning/blob/0cc458e237c19a725d57ed33b3abe90dd7a0d3a4/src/lightning/pytorch/plugins/precision/fsdp.py#L36-L43 and https://github.com/Lightning-AI/lightning/blob/0cc458e237c19a725d57ed33b3abe90dd7a0d3a4/src/lightning/pytorch/trainer/connectors/accelerator_connector.py#L542-L544

Thanks for all your continued work making Lightning better every day!
@awaelchli @carmocca

[awaelchli]

@speediedan #17670 was a different issue. We definitely want to bring support for 16-true to the Lightning Trainer (#17609) and with it also in the special FSDP precision plugin. What you point out is the change required to make the plugin accept the strings, and that's basically what I opened this ticket for, just for the Fabric side of things. But yes, it applies to both Fabric and PyTorch :)

[speediedan]

Awesome, figured it was all planned but thanks for thorough (as always!) clarification @awaelchli! Reminds me I'm looking forward to contributing/collaborating with you guys more in the future!