docs: finish swarm-cli migration for installation/faq/api docs (rebase of curl-to-swarm-cli branch)

[yjkellyjoo]

Problem

docs/bee/working-with-bee/introduction.md and docs/bee/working-with-bee/swarm-cli.md already recommend swarm-cli as the primary way to interact with a Bee node from the command line.

Several other pages haven't caught up: they still show raw curl/jq calls against the Bee API where a swarm-cli command would now do the same job.

Prior attempt

Branch curl-to-swarm-cli (pushed to origin, no PR ever opened) already drafted this migration for:

• docs/bee/faq.md
• docs/bee/installation/docker.md
• docs/bee/installation/fund-your-node.md
• docs/bee/installation/getting-started.md
• docs/bee/installation/package-manager.md
• docs/bee/installation/shell-script.md
• docs/bee/working-with-bee/bee-api.md
• docs/bee/working-with-bee/swarm-cli.md
• src/css/custom.css

Treat this branch as a draft reference only, not a mergeable diff. Its last commit is from 2025-05-15, and master has moved roughly 287 commits past the branch's merge-base since. Content, line numbers, and even some swarm-cli/Bee API command output shown in the draft may be stale.

Scope of this issue

• Rebase/refresh the draft against current master.
• Re-verify every swarm-cli command and Bee API example against current swarm-cli and Bee behavior before reusing it from the draft (flags, output formatting, and defaults may have changed since May 2025).
• Split into per-file commits/PRs as appropriate. This issue can be broken into further sub-issues once someone starts the work.

Out of scope

• docs/bee/working-with-bee/cashing-out.md — tracked separately in docs: replace stale cashout script with swarm-cli in "Managing uncashed cheques" #836 (the "Managing uncashed cheques" section), which the old branch never touched.
• Incidental defects noticed along the way, e.g. the dangling * Add stake: bullet at docs/bee/working-with-bee/swarm-cli.md:16 noted in docs: replace stale cashout script with swarm-cli in "Managing uncashed cheques" #836 — file those separately rather than folding them in here.

Related

• Parent epic: ethersphere/DevRel#899
• Sibling: docs: replace stale cashout script with swarm-cli in "Managing uncashed cheques" #836