chore(ci): stop auto-deploying staging-public on nightly tag

[AztecBot]

Summary

Drops the workflow_run trigger on .github/workflows/deploy-staging-public.yml so the nightly tag no longer kicks off a staging-public deploy. workflow_dispatch is kept so the workflow can still be hand-run from the Actions UI if needed.

Requested in #alerts-staging-public — "we don't want staging-public to deploy anymore".

Context: the run that failed last night

The most recent run (26325263985) failed in the reusable deploy / deploy-network job's Checkout step, before any cluster work. Submodule init aborted because every clone hit:

fatal: could not read Username for 'https://github.com': terminal prompts disabled
fatal: expected flush after ref listing

…and the retry loop also failed (Failed to clone 'l1-contracts/lib/circuits' a second time, aborting). All affected submodules are public repos, so the symptom is GitHub's HTTPS endpoint refusing unauthenticated requests and the credential header actions/checkout set up for the parent clone not being applied to the submodule URLs. Run #104 (2026-05-22, commit 87aa5283) failed the same way, so it isn't a one-off flake — but since staging-public is being retired, fixing the checkout config in deploy-network.yml is out of scope here. Filing separately if needed for testnet / next-net / mainnet, which share the same job.

Test plan

• After merge, confirm the next "Nightly Release Tag (v4-next)" completion does not trigger a "Deploy to staging-public" workflow run.
• Confirm the workflow is still listed under Actions and can be manually dispatched from the UI.

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Created by claudebox · group: slackbot

[alexghr]

this is already contained in merge-train/spartan