exp list: does not show new experiments

Bug Report

Description

When the terminal is killed while dvc exp run is executing, the ref .git/refs/exps/exec/EXEC_BASELINE is not removed.
Then when a git commit is made, git might pack the references to optimize performance.
Now, dvc exp list is stuck with the list of experiments before the commit and will not update when new experiments are run.

This also affects the experiments table in the vscode extension.

Reproduce

1. git init
2. dvc init
3. dvc stage add -n prepare -d prepare.py python prepare.py
4. create file prepare.py and write a program that takes some time (e.g. time.sleep(10))
5. git add .
6. git commit -m "commit 1"
7. dvc exp run
8. while running: Kill the terminal (not via ctrl+c but by closing the terminal)
9. edit prepare.py (to make dvc exp run execute the pipeline again)
10. git add .
11. git commit -m "commit 2"
12. git pack-refs --all: when committing, git sometimes does "git pack-refs" for optimization. It can happen right here. To simulate the automatic packing, run git pack-refs --all
13. dvc exp run
14. dvc exp list

Expected

dvc exp list should show the experiment from 13. Instead, it returns nothing.
It only shows the experiment with dvc exp list -A

Environment information

Output of dvc doctor:

$ dvc doctor
DVC version: 2.38.1 (exe)
---------------------------------
Platform: Python 3.10.9 on Windows-10-10.0.19045-SP0
Subprojects:

Supports:
        azure (adlfs = 2022.11.2, knack = 0.10.1, azure-identity = 1.12.0),
        gdrive (pydrive2 = 1.15.0),
        gs (gcsfs = 2022.11.0),
        hdfs (fsspec = 2022.11.0, pyarrow = 10.0.1),
        http (aiohttp = 3.8.3, aiohttp-retry = 2.8.3),
        https (aiohttp = 3.8.3, aiohttp-retry = 2.8.3),
        oss (ossfs = 2023.1.0),
        s3 (s3fs = 2022.11.0, boto3 = 1.24.59),
        ssh (sshfs = 2022.6.0),
        webdav (webdav4 = 0.9.8),
        webdavs (webdav4 = 0.9.8),
        webhdfs (fsspec = 2022.11.0)
Cache types: <https://error.dvc.org/no-dvc-cache>
Caches: local
Remotes: None
Workspace directory: NTFS on C:\
Repo: dvc, git

Reproduce the issue using the listed git and DVC commands, especially the packed refs step, then start from the dvc exp list entry point and compare it with dvc exp list -A. Done means a newly run experiment appears in the default listing after refs are packed, and the VS Code experiments table is no longer affected.