fix(browser): normalize empty instance names

[Mercy811]

Summary

• Add a shared Analytics Core normalizer so undefined and exactly '' resolve to $default_instance.
• Make connector lookup defensive and retain the normalized value in BrowserConfig.
• Route Browser Analytics initialization and identity updates through the normalized connector.
• Let the Browser Experiment plugin inherit the Analytics instance name unless explicitly overridden.
• Add regression coverage for default, empty, custom, whitespace, and explicit-override cases.

Why

Browser Analytics could bind identity and its event receiver to an empty-string connector while Experiment resolved the same input to $default_instance. The SDKs would initialize successfully but silently lose identity synchronization and Experiment exposure-event forwarding.

PR #1944 fixed the React Native occurrence that exposed this issue. This PR applies the corresponding Browser/Core fix tracked by SDKW-59.

Safety and storage impact

• A full packages/analytics-browser search found that the configured instance name only routes in-memory connector activity.
• The similarly named snippet createInstance(instanceName) registry is separate and is not changed.
• The Analytics Connector stores identity, listeners, its receiver, and its bounded event queue only in memory under globalThis.analyticsConnectorInstances.
• Browser identity/session, unsent-event, and attribution storage keys are based on the API key, not instanceName; no persistent storage migration is involved.
• Non-empty custom names remain isolated and unchanged. Whitespace-only names are intentionally not trimmed.

Validation

• Analytics Core: 884 tests passed, 100% coverage.
• Browser Analytics: 509 tests passed, 100% coverage.
• Browser Experiment plugin: 12 tests passed, 100% coverage.
• Typecheck and lint passed for all three affected packages.

Ticket: https://linear.app/amplitude/issue/SDKW-59/normalize-empty-instancename-across-browser-analytics-and-experiment

[linear-code]

SDKW-59

[github-actions]

size-limit report 📦

Path	Size
packages/analytics-browser/lib/scripts/amplitude-min.js.gz	64.28 KB (+0.01% 🔺)
packages/session-replay-browser/lib/scripts/session-replay-browser-min.js.gz	134.98 KB (+0.01% 🔺)
packages/unified/lib/scripts/amplitude-min.umd.js.gz	218.42 KB (+0.02% 🔺)
@amplitude/element-selector (gzipped esm)	3.4 KB (0%)