feat: push each site's online set into the network summary

[josephfusco]

Part of the network presence stack, merged bottom-up:

1. feat: add a network-wide presence summary table #332 summary table
2. feat: push each site's online set into the network summary #333 write path (this one)
3. feat: read the network summary as a capped snapshot #334 read path
4. feat: add an Online column to the Network Sites list #335 Sites list column
5. feat: add an Online view and column to the Network Users list #336 Users list
6. feat: add a Who's Online widget to the Network Admin dashboard #337 network dashboard widget

---

The table in #332 has nothing writing into it.

Part of #298
Closes #327

Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Claude Sonnet 5, Claude Opus 5
Used for: Assisting with design, implementation, and testing

[github-actions]

The following accounts have interacted with this PR and/or linked issues. I will continue to update these lists as activity occurs. You can also manually ask me to refresh this list by adding the props-bot label.

Core Committers: Use this line as a base for the props when committing in SVN:

Props iamchitti, joefusco.

To understand the WordPress project's expectations around crediting contributors, please review the Contributor Attribution page in the Core Handbook.

[github-actions]

▶ Preview in WordPress Playground

Boots a fresh WordPress with this PR's presence-api build, seeds 5 demo users, and drops you on the dashboard.

_{Stress-test variant: 40 demo users · Built from 6c1549be2d019605fd31de508cba208bb56a1f7c. Auto-updates when you push.}

[josephfusco]

Review findings from #299 that land here are #310, answered by the debounce, plus #329 and #343, which are not fixed.

[codecov]

Codecov Report

❌ Patch coverage is 96.66667% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.98%. Comparing base (6173f42) to head (6c1549b).

Additional details and impacted files

@@                         Coverage Diff                         @@
##             feature/network-summary-table     #333      +/-   ##
===================================================================
+ Coverage                            94.33%   96.98%   +2.65%     
  Complexity                             190      190              
===================================================================
  Files                                   15       15              
  Lines                                 2099     2159      +60     
===================================================================
+ Hits                                  1980     2094     +114     
+ Misses                                 119       65      -54     

Flag	Coverage Δ
multisite	96.98% <96.66%> (?)
phpunit	92.07% <13.33%> (-2.26%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.