`start_server` context manager not idempotent

[sternj]

The below is adapted from the Rust tests. I expect both printouts to be identical, but the second prints None.

from multilspy.multilspy_config import MultilspyConfig
from multilspy.multilspy_logger import MultilspyLogger
from multilspy.multilspy_utils import FileUtils
from multilspy import SyncLanguageServer
from tempfile import TemporaryDirectory
import os
from pathlib import Path, PurePath

params = {
    "code_language": "rust",
    "repo_url": "https://github.com/fathyb/carbonyl/",
    "repo_commit": "ab80a276b1bd1c2c8dcefc8f248415dfc61dc2bf",
}
config = MultilspyConfig.from_dict(params)
logger = MultilspyLogger()

with TemporaryDirectory() as temp_dir:
    repo_zip_url = params["repo_url"] + f"archive/{params['repo_commit']}.zip"
    FileUtils.download_and_extract_archive(logger, repo_zip_url, temp_dir, "zip")
    dir_contents = os.listdir(temp_dir)
    assert len(dir_contents) == 1
    source_directory_path = str(Path(temp_dir, dir_contents[0]))
    lsp = SyncLanguageServer.create(config, logger, source_directory_path)
    with lsp.start_server():
        print(
            "FIRST RESULT",
            lsp.request_hover(str(PurePath("src/browser/bridge.rs")), 132, 18),
        )
    with lsp.start_server():
        print(
            "SECOND RESULT",
            lsp.request_hover(str(PurePath("src/browser/bridge.rs")), 132, 18),
        )