[Bug]: Clang-Tidy outputs absolute filepaths

### What happened?

When running `bazel lint //speller/...` I am seeing absolute filepaths (which include the bazel output tree) with the linting results:
```
/private/var/tmp/_bazel_jesse/93d7e699c5e2019d94351d19b00be5a3/sandbox/darwin-sandbox/11/execroot/_main/speller/data_driven_tests/lookup-datatest.cc:16:8: warning: an exception may be thrown in function 'test_config' which should not throw exceptions [bugprone-exception-escape]
```

I expected to see relative filepaths outputed instead:
```
speller/data_driven_tests/lookup-datatest.cc:16:8: warning: an exception may be thrown in function 'test_config' which should not throw exceptions [bugprone-exception-escape]
```

### Version

Development (host) and target OS/architectures:

Reproduceable on MacOS and Ubuntu

Output of `bazel --version`:

(This happens on all versions of the Aspect CLI)
```
Bazelisk version: 1.20.0
Aspect CLI Pro version: 5.11.0-alpha0.dev.150.g12ded54
Build label: 7.3.1
Build target: @@//src/main/java/com/google/devtools/build/lib/bazel:BazelServer
Build time: Mon Aug 19 16:41:27 2024 (1724085687)
Build timestamp: 1724085687
Build timestamp as int: 1724085687
```

Version of the Aspect rules, or other relevant rules from your
`WORKSPACE` or `MODULE.bazel` file:

```
bazel_dep(name = "aspect_bazel_lib", version = "2.7.7")
bazel_dep(name = "aspect_rules_cypress", version = "0.6.0")
bazel_dep(name = "aspect_rules_esbuild", version = "0.21.0")
bazel_dep(name = "aspect_rules_jasmine", version = "2.0.0")
bazel_dep(name = "aspect_rules_jest", version = "0.22.0")
bazel_dep(name = "aspect_rules_js", version = "2.0.0")
bazel_dep(name = "aspect_rules_lint", version = "1.0.0-rc9")
bazel_dep(name = "aspect_rules_swc", version = "2.0.0")
bazel_dep(name = "aspect_rules_ts", version = "3.0.0")
bazel_dep(name = "aspect_rules_webpack", version = "0.16.0")
```

Language(s) and/or frameworks involved:

Clang-Tidy

### How to reproduce

```shell
Checkout: https://github.com/aspect-build/bazel-examples

Run: `bazel lint //speller/...`
```

### Any other information?

We have solved this problem for eslint. Look into how we fixed it there and apply it to clang tidy as well

Reproduce the issue with `bazel lint //speller/...` in the bazel-examples checkout, then inspect how the existing eslint fix produces relative paths. Compare that path handling with the Clang-Tidy integration and verify that lint output uses workspace-relative paths for the speller targets.

Written by the indexing model from the issue text.