Rollup merge of #149850 - GuillaumeGomez:rm-tidy-rustdoc, r=yotamofek

Remove "tidy" tool for `tests/rustdoc` testsuite

As discussed in the [last rustdoc meeting](https://rust-lang.zulipchat.com/#narrow/channel/393423-t-rustdoc.2Fmeetings/topic/2025-12-08/near/562554410), it seems like the current `tidy` tool is not used much for the `rustdoc` testsuite by the rustdoc contributors as it doesn't fit nicely our needs.

Until we find something better, we decided to remove it.

r? ```@yotamofek```

Author: matthiaskrgr