[llvm] [CodeGen][NewPM] Port `LiveIntervals` to new pass manager (PR #98118)

[via llvm-commits]

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@@ -50,445 +51,492 @@ class raw_ostream;
 class TargetInstrInfo;
 class VirtRegMap;
 
-  class LiveIntervals : public MachineFunctionPass {
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paperchalice wrote:

`clang-format` formats almost entire class after modifying this line.

https://github.com/llvm/llvm-project/pull/98118