[Local Catalog] POS Settings: integrate with catalog data and full sync functionality

[jaclync]

Part of WOOMOB-1100
Please review #16166 first, or together.

Description

This PR integrates the settings UI with catalog stats & sync functionality. The implementation includes:

• POSSettingsLocalCatalogViewModel: A view model that handles the UI logic for displaying catalog info and triggering full sync from CTA tap
• Test coverage: Unit tests for both the view model and service with proper date comparison handling due to different precision in the database

Steps to reproduce

1. Log in to a store eligible for POS if needed
2. Tap on the POS tab
3. Tap the ellipsis menu > Settings > Catalog --> the catalog size, incremental sync date, full sync date should be accurate
4. In wp-admin, add a product/variation
5. Tap on Refresh catalog to start a full sync --> the spinner should be shown in the button. for a site with a small catalog, it should be rather quick. the catalog size & last full sync date should be updated after the sync completes

Testing information

I tested on a small site, and a large site and left the settings while the full sync was still ongoing.

Screenshots

Latest copy:

Simulator.Screen.Recording.-.iPad.A16.-.2025-09-18.at.16.29.12.mov

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• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

[wpmobilebot]

📲 You can test the changes from this Pull Request in WooCommerce iOS Prototype by scanning the QR code below to install the corresponding build.

	App Name	WooCommerce iOS Prototype
	Build Number	pr16144-6293042
	Version	23.3
	Bundle ID	com.automattic.alpha.woocommerce
	Commit	6293042
	Installation URL	6rubgov2tf8d8

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[jaclync]

Hi @joshheald no rush reviewing this PR, or just leave initial comments first on a high level review if you get a chance. I will try breaking it into two PRs if you will be reviewing it later.

[joshheald]

Generally looks great, thanks for doing this.

I found that when I switched stores, the old numbers were used. I can't immediately see why, but it only happened if I was quick to open POS, and corrected itself after closing and re-opening POS. So there's some state sticking around between launches. The sync coordinator is suspect here, because it's held on the service locator... but it shouldn't really play a part in getting the numbers, so perhaps there's something else that's not reset when it should be.

Also, we use "Last incremental update" and "Last full sync" as titles, which is inconsistent. I think it would stand out less if we just said "Last update", which is clearer anyway, or "Last incremental sync", though I like that less.

[jaclync]

I found that when I switched stores, the old numbers were used. I can't immediately see why, but it only happened if I was quick to open POS, and corrected itself after closing and re-opening POS. So there's some state sticking around between launches. The sync coordinator is suspect here, because it's held on the service locator... but it shouldn't really play a part in getting the numbers, so perhaps there's something else that's not reset when it should be.

I noticed this issue during testing as well, it was from a recent CIAB change p1758613264239289/1758605672.214159-slack-CGPNUU63E. Kiwi had a workaround p1758690950124649/1758605672.214159-slack-CGPNUU63E and I had a PR #16173 that refactors this part. I will merge after testing with the latest trunk merged in.

[jaclync]

Also, we use "Last incremental update" and "Last full sync" as titles, which is inconsistent. I think it would stand out less if we just said "Last update", which is clearer anyway, or "Last incremental sync", though I like that less.

If I understood correctly, I made the following copy changes to show "sync" instead of "sync" in the UI:

• "Last incremental update" → "Last update"
• "Last full sync" → "Last full update" (to match the pattern)

Along with other changes to use "update" for consistency in aba8530. We don't have a design for the settings yet, can make more copy/UI updates later.