rustdoc: Separate the caches for synthetic auto trait & blanket impls

[fmease]

Fixes #148980.

[fmease]

@bors try @rust-timer queue

[rust-bors]

☀️ Try build successful (CI)
Build commit: f14d268 (f14d2688a5033df0ddc0f711bc16c01326d36654, parent: c58275e0369d09fc3959b8ba87dcbcbe73797465)

[rust-timer]

Finished benchmarking commit (f14d268): comparison URL.

Overall result: ✅ improvements - no action needed

Benchmarking means the PR may be perf-sensitive. Consider adding rollup=never if this change is not fit for rolling up.

@rustbot label: -S-waiting-on-perf -perf-regression

Instruction count

Our most reliable metric. Used to determine the overall result above. However, even this metric can be noisy.

	mean	range	count
Regressions ❌ (primary)	-	-	0
Regressions ❌ (secondary)	-	-	0
Improvements ✅ (primary)	-	-	0
Improvements ✅ (secondary)	-0.0%	[-0.0%, -0.0%]	1
All ❌✅ (primary)	-	-	0

Max RSS (memory usage)

Results (secondary -5.5%)

A less reliable metric. May be of interest, but not used to determine the overall result above.

	mean	range	count
Regressions ❌ (primary)	-	-	0
Regressions ❌ (secondary)	-	-	0
Improvements ✅ (primary)	-	-	0
Improvements ✅ (secondary)	-5.5%	[-5.5%, -5.4%]	2
All ❌✅ (primary)	-	-	0

Cycles

Results (primary 2.4%, secondary 3.9%)

A less reliable metric. May be of interest, but not used to determine the overall result above.

	mean	range	count
Regressions ❌ (primary)	2.4%	[2.3%, 2.5%]	2
Regressions ❌ (secondary)	3.9%	[3.9%, 3.9%]	1
Improvements ✅ (primary)	-	-	0
Improvements ✅ (secondary)	-	-	0
All ❌✅ (primary)	2.4%	[2.3%, 2.5%]	2

Binary size

Results (primary -0.1%, secondary -0.1%)

A less reliable metric. May be of interest, but not used to determine the overall result above.

	mean	range	count
Regressions ❌ (primary)	-	-	0
Regressions ❌ (secondary)	-	-	0
Improvements ✅ (primary)	-0.1%	[-0.1%, -0.0%]	19
Improvements ✅ (secondary)	-0.1%	[-0.1%, -0.0%]	18
All ❌✅ (primary)	-0.1%	[-0.1%, -0.0%]	19

Bootstrap: 515.367s -> 515.314s (-0.01%)
Artifact size: 400.82 MiB -> 400.68 MiB (-0.03%)