fix: on-demand downloads can outlive timeline shutdown (#7051)

## Problem

Before this PR, it was possible that on-demand downloads were started
after `Timeline::shutdown()`.

For example, we have observed a walreceiver-connection-handler-initiated
on-demand download that was started after `Timeline::shutdown()`s final
`task_mgr::shutdown_tasks()` call.

The underlying issue is that `task_mgr::shutdown_tasks()` isn't sticky,
i.e., new tasks can be spawned during or after
`task_mgr::shutdown_tasks()`.

Cc: https://github.com/neondatabase/neon/issues/4175 in lieu of a more
specific issue for task_mgr. We already decided we want to get rid of it
anyways.

Original investigation:
https://neondb.slack.com/archives/C033RQ5SPDH/p1709824952465949

## Changes

- enter gate while downloading
- use timeline cancellation token for cancelling download

thereby, fixes #7054

Entering the gate might also remove recent "kept the gate from closing"
in staging.

test_runner/regress/test_tenant_delete.py

@@ -190,6 +190,8 @@ def test_delete_tenant_exercise_crash_safety_failpoints(
             # So by ignoring these instead of waiting for empty upload queue
             # we execute more distinct code paths.
             '.*stopping left-over name="remote upload".*',
+            # an on-demand is cancelled by shutdown
+            ".*initial size calculation failed: downloading failed, possibly for shutdown",
         ]
     )
 

test_runner/regress/test_timeline_delete.py

@@ -213,7 +213,9 @@ def test_delete_timeline_exercise_crash_safety_failpoints(
             # This happens when timeline remains are cleaned up during loading
             ".*Timeline dir entry become invalid.*",
             # In one of the branches we poll for tenant to become active. Polls can generate this log message:
-            f".*Tenant {env.initial_tenant} is not active*",
+            f".*Tenant {env.initial_tenant} is not active.*",
+            # an on-demand is cancelled by shutdown
+            ".*initial size calculation failed: downloading failed, possibly for shutdown",
         ]
     )