Replace Umami analytics with the new Analytics battery

[notheotherben]

Summary

Umami analytics is being retired in favor of the new self-hosted analytics server at https://analytics.sierrasoftworks.com. This PR migrates github-backup to the tracing-batteries Analytics battery, which replaces the old Umami battery.

• Swapped the tracing-batteries cargo feature flag from umami to analytics in Cargo.toml.
• Replaced Umami::new(server_url, website_id).with_initial_page("/.app/") with Analytics::new(server_url). The new battery takes only the server URL (no website ID) and no longer needs the /.app/ page-prefix convention — it defaults to page / on a virtual hostname of {service}.app.
• Updated the use tracing_batteries::{...} import accordingly.
• Bumped Cargo.lock via cargo update tracing-batteries to pull in the latest main of the tracing-batteries-rs git dependency, which ships the Analytics battery.

No changes were needed to the existing session.record_new_page(format!("/backup/{}", policy)) call — it already uses a clean path.

Test plan

• cargo check passes
• cargo clippy --all-targets passes with no warnings
• cargo test — 111 passed; 6 pre-existing failures unrelated to this change (network/TLS errors reaching api.github.com from the sandbox, in GitHub API test helpers, not the analytics code)

🤖 Generated with Claude Code

https://claude.ai/code/session_01NutKW958x2VF9rVagycenv

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Generated by Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 0% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 73.25%. Comparing base (3b44c02) to head (1dd6df6).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/main.rs	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #615      +/-   ##
==========================================
+ Coverage   73.18%   73.25%   +0.06%     
==========================================
  Files          30       30              
  Lines        2111     2109       -2     
==========================================
  Hits         1545     1545              
+ Misses        566      564       -2     

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