Repository: iterative/dvc

Issue:
exp init: exclude `metrics.json` and `plots` from default paths in `dvc exp init --type=live`
# Bug Report

## Description

When using the `live` type in `dvc exp init`, `metrics.json` and `plots` appear under the default paths in interactive mode when showing the assumed workspace structure.

Also, `plots` is included as an output in non-interactive mode.

### Reproduce

```
$ dvc exp init -f -i --type=live python src/train.py
This command will guide you to set up a live stage in dvc.yaml.
See https://dvc.org/doc/user-guide/project-structure/pipelines-files.

Enter the paths for dependencies and outputs of the command.
DVC assumes the following workspace structure:
├── data
├── dvclive
├── metrics.json
├── models
├── params.yaml
├── plots
└── src

Path to a code file/directory [src, n to omit]:
'src' does not exist in the workspace. "exp run" may fail.
Path to a data file/directory [data, n to omit]:
'data' does not exist in the workspace. "exp run" may fail.
Path to a model file/directory [models, n to omit]:
Path to a parameters file [params.yaml, n to omit]:
Path to log dvclive outputs [dvclive, n to omit]:
─────────────────────────────────────────────────────────────────────────────────────────
live:
  cmd: python src/train.py
  deps:
  - data
  - src
  params:
  - foo
  outs:
  - models:
      checkpoint: true
  live:
    dvclive:
      summary: true
      html: true

Do you want to add the above contents to dvc.yaml? [Y/n] Y

Created live stage in dvc.yaml. To run, use "dvc exp run".
See https://dvc.org/doc/user-guide/experiment-management/running-experiments.

$ cat dvc.yaml
stages:
  live:
    cmd: python src/train.py
    deps:
    - data
    - src
    outs:
    - models:
        checkpoint: true
    live:
      dvclive:
        summary: true
        html: true
    params:
    - foo
```

Also, the `plots` output is included by default when using `live` type but not interactive mode:

```
$ dvc exp init -f --type=live python src/train.py
Created live stage in dvc.yaml. To run, use "dvc exp run".
See https://dvc.org/doc/user-guide/experiment-management/running-experiments.

$ cat dvc.yaml
stages:
  live:
    cmd: python src/train.py
    deps:
    - data
    - src
    outs:
    - models:
        checkpoint: true
    live:
      dvclive:
        summary: true
        html: true
    plots:
    - plots:
        cache: false
```

### Expected

```
$ dvc exp init -f -i --type=live python src/train.py
This command will guide you to set up a live stage in dvc.yaml.
See https://dvc.org/doc/user-guide/project-structure/pipelines-files.

Enter the paths for dependencies and outputs of the command.
DVC assumes the following workspace structure:
├── data
├── dvclive
├── models
├── params.yaml
└── src

Path to a code file/directory [src, n to omit]:
'src' does not exist in the workspace. "exp run" may fail.
Path to a data file/directory [data, n to omit]:
'data' does not exist in the workspace. "exp run" may fail.
Path to a model file/directory [models, n to omit]:
Path to a parameters file [params.yaml, n to omit]:
Path to log dvclive outputs [dvclive, n to omit]:
─────────────────────────────────────────────────────────────────────────────────────────
live:
  cmd: python src/train.py
  deps:
  - data
  - src
  params:
  - foo
  outs:
  - models:
      checkpoint: true
  live:
    dvclive:
      summary: true
      html: true

Do you want to add the above contents to dvc.yaml? [Y/n] Y

Created live stage in dvc.yaml. To run, use "dvc exp run".
See https://dvc.org/doc/user-guide/experiment-management/running-experiments.

$ cat dvc.yaml
stages:
  live:
    cmd: python src/train.py
    deps:
    - data
    - src
    outs:
    - models:
        checkpoint: true
    live:
      dvclive:
        summary: true
        html: true
    params:
    - foo
```

```
$ dvc exp init -f --type=live python src/train.py
Created live stage in dvc.yaml. To run, use "dvc exp run".
See https://dvc.org/doc/user-guide/experiment-management/running-experiments.

$ cat dvc.yaml
stages:
  live:
    cmd: python src/train.py
    deps:
    - data
    - src
    outs:
    - models:
        checkpoint: true
    live:
      dvclive:
        summary: true
        html: true
```


Discussion:
The `plots` definitely is due to a typo, the following should be `plots` instead:
https://github.com/iterative/dvc/blob/264d78b637690f541ee1e4a7ca73b433afb383dd/dvc/repo/experiments/init.py#L307

Resolving patch:
diff --git a/dvc/repo/experiments/init.py b/dvc/repo/experiments/init.py
--- a/dvc/repo/experiments/init.py
+++ b/dvc/repo/experiments/init.py
@@ -215,6 +215,9 @@ def init_interactive(
         )
         if not live and "live" not in provided:
             workspace.pop("live", None)
+        for key in ("plots", "metrics"):
+            if live and key not in provided:
+                workspace.pop(key, None)
         for value in sorted(workspace.values()):
             tree.add(f"[green]{value}[/green]")
         ui.error_write(tree, styled=True)


Test patch: