Remove random sleep in partial backup

[petuhovskiy]

We had a random sleep in the beginning of partial backup task, which was needed for the first partial backup deploy. It helped with gradual upload of segments without causing network overload. Now partial backup is deployed everywhere, so we don't need this random sleep anymore.

We also had an issue related to this, in which manager task was not shut down for a long time. The cause of the issue is this random sleep that didn't take timeline cancellation into account, meanwhile manager task waited for partial backup to complete.

Fixes #7967

[github-actions]

3210 tests run: 3071 passed, 0 failed, 139 skipped (full report)

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Flaky tests (6)

Postgres 16

• test_storage_controller_smoke: debug

Postgres 15

• test_pageserver_restarts_under_worload: release
• test_storage_controller_smoke: debug
• test_vm_bit_clear_on_heap_lock: debug

Postgres 14

• test_pageserver_restarts_under_worload: release
• test_subscriber_restart: release

Code coverage* (full report)

• functions: 31.5% (6596 of 20927 functions)
• lines: 48.5% (51050 of 105267 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
35b5bba at 2024-06-06T18:02:56.535Z :recycle:}