refactor(timings): separate data collection and presentation

[weihanglo]

What does this PR try to resolve?

The goal of this refactor is to separate data collection and presentation,
so that we can replay an HTML report from log generated by -Zbuild-analysis.

Part of #15844

How to test and review this PR?

Should have no user-facing change,
though I would encourage review to run cargo build --timings
and check if there is anything broken.

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[weihanglo]

We probably have seen this on Windows aarch64 MSVC stable? (I totally forgot)

https://github.com/rust-lang/cargo/actions/runs/19555803247/job/55997837387#step:15:4835

thread 'registry::sparse_blocking_count' (1028) panicked at tests\testsuite\registry.rs:3587:7:

---- expected: tests\testsuite\registry.rs:3572:27
++++ actual:   stderr
   1      -    [..] TRACE network::HttpRegistry::block_until_ready: 0 transfers pending
        1 +   11.521002200s TRACE network::HttpRegistry::block_until_ready: 0 transfers pending
   2    2 | [UPDATING] `dummy-registry` index
   3      -    [..] TRACE network::HttpRegistry::block_until_ready: 1 transfers pending
   4      -    [..] TRACE network::HttpRegistry::block_until_ready: 1 transfers pending
        3 +   11.522428200s TRACE network::HttpRegistry::block_until_ready: 1 transfers pending
        4 +   11.526991600s TRACE network::HttpRegistry::block_until_ready: 1 transfers pending
   5    5 | [WARNING] spurious network error (3 tries remaining): failed to get successful HTTP response from `[..]/index/3/b/bar` ([..]), got 500
   6    6 | body:
   7    7 | internal server error
   8    8 | [LOCKING] 1 package to latest compatible version
   9    9 | [DOWNLOADING] crates ...
  10   10 | [DOWNLOADED] bar v0.0.1 (registry `dummy-registry`)
  11   11 | [CHECKING] bar v0.0.1
  12   12 | [CHECKING] foo v0.0.1 ([ROOT]/foo)
  13   13 | [FINISHED] `dev` profile [unoptimized + debuginfo] target(s) in [ELAPSED]s