The change in lock logic for `partialCached` in 0927cf739f was naive as it didn't consider cached partials calling other cached partials.
This changeset may look on the large side for this particular issue, but it pulls in part of a working branch, introducing `context.Context` in the template execution.
Note that the context is only partially implemented in this PR, but the upcoming use cases will, as one example, include having access to the top "dot" (e.g. `Page`) all the way down into partials and shortcodes etc.
The earlier benchmarks rerun against master:
```bash
name old time/op new time/op delta
IncludeCached-10 13.6ms ± 2% 13.8ms ± 1% ~ (p=0.343 n=4+4)
name old alloc/op new alloc/op delta
IncludeCached-10 5.30MB ± 0% 5.35MB ± 0% +0.96% (p=0.029 n=4+4)
name old allocs/op new allocs/op delta
IncludeCached-10 74.7k ± 0% 75.3k ± 0% +0.77% (p=0.029 n=4+4)
```
Fixes#9519
929808190f