remove old update mechanism

[marcoieni]

• I did not use an LLM to create a change in this PR.
• I used an LLM to create a change in this PR, and I have explained below how it was used.

The old update mechanism doesn't work anymore since we switched to GitHub rulesets. We replaced it with Renovate. See rust-lang/infra-team#293

LLMs

I used LLMs by asking to delete the previous update mechanism.

I think my use of LLMs in this case can be categorized under “Trivial” code, so I guess it's fine.

[rustbot]

r? @Mark-Simulacrum

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The reviewer was selected based on:

• Owners of files modified in this PR: infra-ci
• infra-ci expanded to Kobzol, Mark-Simulacrum, jdno, jieyouxu, marcoieni
• Random selection from Mark-Simulacrum, jdno