Repository: iterative/dvc (python)

Issue:
`dvc studio login`: setup auto pushing experiments
See #5029 and the related issues linked there for background.

Rather than document the environment variables to auto push experiments, we could make this part of the studio login workflow since auto-pushing experiments is mostly useful when using studio rather than keeping experiments local. We would need to:

1. Make config options like `exp.auto_push` and `exp.git_remote`
2. During studio login, ask to set these variables. The UI could look something like this: 

```sh
$ dvc studio login
...
Authentication successful. The token will be available as risen-geum in Studio profile.
Do you want to push experiments automatically when they are completed [Y\n]?
Enter the Git remote name to use [origin]:
```

Pull request description:
exp: use exp git remote for studio repo url
Simplifies setting studio repo url per the suggestion [here](https://github.com/iterative/dvc.org/pull/5165#discussion_r1512677465).

If `DVC_EXP_GIT_REMOTE` env var or `dvc config exp.git_remote` is set, the url for that remote will be set for sending updates to Studio and override `DVC_STUDIO_REPO_URL`/`studio.repo_url` (these can be deprecated and dropped in the future).

Closes #10137

- [x] Docs PR: https://github.com/iterative/dvc.org/pull/5178
- [x] Look whether DVCLive changes are needed: https://github.com/iterative/dvclive/pull/799

Patch:
diff --git a/dvc/repo/experiments/executor/base.py b/dvc/repo/experiments/executor/base.py
index 933353b57..64b670c80 100644
--- a/dvc/repo/experiments/executor/base.py
+++ b/dvc/repo/experiments/executor/base.py
@@ -25,6 +25,7 @@ from dvc.utils import dict_sha256, env2bool, relpath
 from dvc.utils.fs import remove
 from dvc.utils.studio import (
     env_to_config,
+    get_repo_url,
     get_subrepo_relpath,
 )
 
@@ -611,6 +612,8 @@ class BaseExecutor(ABC):
             # inferring repo url will fail if not set here
             run_env_config = env_to_config(kwargs.get("run_env", {}))
             dvc_studio_config = run_env_config | dvc_studio_config
+            # override studio repo url if exp git remote set
+            repo_url = get_repo_url(dvc)
             try:
                 post_live_metrics(
                     "start",
@@ -621,6 +624,7 @@ class BaseExecutor(ABC):
                     dvc_studio_config=dvc_studio_config,
                     message=message,
                     subdir=get_subrepo_relpath(dvc),
+                    studio_repo_url=repo_url,
                 )
                 logger.debug("Running repro in '%s'", os.getcwd())
                 yield dvc
@@ -646,6 +650,7 @@ class BaseExecutor(ABC):
                     experiment_rev=dvc.experiments.scm.get_ref(EXEC_BRANCH),
                     metrics=_gather_metrics(dvc, on_error="return"),
                     dvc_studio_config=dvc_studio_config,
+                    studio_repo_url=repo_url,
                 )
 
                 if infofile is not None:
diff --git a/dvc/utils/studio.py b/dvc/utils/studio.py
index 470d19549..13065c291 100644
--- a/dvc/utils/studio.py
+++ b/dvc/utils/studio.py
@@ -1,3 +1,4 @@
+import os
 from typing import TYPE_CHECKING, Any, Optional
 from urllib.parse import urljoin
 
@@ -125,3 +126,19 @@ def get_subrepo_relpath(repo: "Repo") -> str:
     relpath = as_posix(repo.fs.relpath(repo.root_dir, scm_root_dir))
 
     return "" if relpath == "." else relpath
+
+
+def get_repo_url(repo: "Repo") -> str:
+    from dulwich.porcelain import get_remote_repo
+
+    from dvc.env import DVC_EXP_GIT_REMOTE
+
+    repo_url = os.getenv(
+        DVC_EXP_GIT_REMOTE, repo.config.get("exp", {}).get("git_remote")
+    )
+    if repo_url:
+        try:
+            _, repo_url = get_remote_repo(repo.scm.dulwich.repo, repo_url)
+        except IndexError:
+            pass
+    return repo_url


Test patch:
diff --git a/tests/integration/test_studio_live_experiments.py b/tests/integration/test_studio_live_experiments.py
index da1136f08..e5851aac7 100644
--- a/tests/integration/test_studio_live_experiments.py
+++ b/tests/integration/test_studio_live_experiments.py
@@ -3,6 +3,7 @@ from dvc_studio_client import env, post_live_metrics
 from funcy import first
 
 from dvc.env import (
+    DVC_EXP_GIT_REMOTE,
     DVC_STUDIO_OFFLINE,
     DVC_STUDIO_REPO_URL,
     DVC_STUDIO_TOKEN,
@@ -16,8 +17,9 @@ from dvc.utils.studio import get_subrepo_relpath
 @pytest.mark.studio
 @pytest.mark.parametrize("tmp", [True, False])
 @pytest.mark.parametrize("offline", [True, False])
+@pytest.mark.parametrize("dvc_exp_git_remote", [None, "DVC_EXP_GIT_REMOTE"])
 def test_post_to_studio(
-    tmp_dir, dvc, scm, exp_stage, mocker, monkeypatch, tmp, offline
+    tmp_dir, dvc, scm, exp_stage, mocker, monkeypatch, tmp, offline, dvc_exp_git_remote
 ):
     valid_response = mocker.MagicMock()
     valid_response.status_code = 200
@@ -28,6 +30,8 @@ def test_post_to_studio(
     monkeypatch.setenv(DVC_STUDIO_TOKEN, "STUDIO_TOKEN")
     monkeypatch.setenv(DVC_STUDIO_URL, "https://0.0.0.0")
     monkeypatch.setenv(DVC_STUDIO_OFFLINE, offline)
+    if dvc_exp_git_remote:
+        monkeypatch.setenv(DVC_EXP_GIT_REMOTE, dvc_exp_git_remote)
 
     baseline_sha = scm.get_rev()
     exp_rev = first(
@@ -52,7 +56,7 @@ def test_post_to_studio(
 
         assert start_call.kwargs["json"] == {
             "type": "start",
-            "repo_url": "STUDIO_REPO_URL",
+            "repo_url": dvc_exp_git_remote or "STUDIO_REPO_URL",
             "baseline_sha": baseline_sha,
             "name": name,
             "params": {"params.yaml": {"foo": 1}},
@@ -61,7 +65,7 @@ def test_post_to_studio(
 
         assert done_call.kwargs["json"] == {
             "type": "done",
-            "repo_url": "STUDIO_REPO_URL",
+            "repo_url": dvc_exp_git_remote or "STUDIO_REPO_URL",
             "baseline_sha": baseline_sha,
             "name": name,
             "client": "dvc",
diff --git a/tests/unit/utils/test_studio.py b/tests/unit/utils/test_studio.py
index 68dcfed77..cc9351ce8 100644
--- a/tests/unit/utils/test_studio.py
+++ b/tests/unit/utils/test_studio.py
@@ -4,12 +4,19 @@ import pytest
 from requests import Response
 
 from dvc.env import (
+    DVC_EXP_GIT_REMOTE,
     DVC_STUDIO_OFFLINE,
     DVC_STUDIO_REPO_URL,
     DVC_STUDIO_TOKEN,
     DVC_STUDIO_URL,
 )
-from dvc.utils.studio import STUDIO_URL, config_to_env, env_to_config, notify_refs
+from dvc.utils.studio import (
+    STUDIO_URL,
+    config_to_env,
+    env_to_config,
+    get_repo_url,
+    notify_refs,
+)
 
 CONFIG = {"offline": True, "repo_url": "repo_url", "token": "token", "url": "url"}
 
@@ -67,3 +74,18 @@ def test_config_to_env():
 
 def test_env_to_config():
     assert env_to_config(ENV) == CONFIG
+
+
+@pytest.mark.parametrize(
+    "exp_git_remote, repo_url",
+    [
+        (None, None),
+        ("origin", "git@url"),
+        ("http://url", "http://url"),
+    ],
+)
+def test_get_repo_url(dvc, scm, monkeypatch, exp_git_remote, repo_url):
+    scm.gitpython.repo.create_remote("origin", "git@url")
+    if exp_git_remote:
+        monkeypatch.setenv(DVC_EXP_GIT_REMOTE, exp_git_remote)
+    assert get_repo_url(dvc) == repo_url