Revise wallet signing and request service logic

[beeman]

Context

PR #994 is scoped to updating @webext-core/proxy-service from 1.2.2 to 2.0.0 and migrating the removed v1 API. During review, CodeRabbit surfaced broader pre-existing signing/request-service concerns that should be handled in a dedicated design pass instead of continuing to expand the dependency PR.

Review context:

• tryCatch/error-boundary feedback: chore(deps): bump @webext-core/proxy-service from 1.2.2 to 2.0.0 #994 (comment)
• active SIWS account mismatch feedback: chore(deps): bump @webext-core/proxy-service from 1.2.2 to 2.0.0 #994 (comment)
• review summary with related secret-key hydration nitpick: chore(deps): bump @webext-core/proxy-service from 1.2.2 to 2.0.0 #994 (review)

Scope to specify

• Define the error contract for background proxy services, including how tryCatch should map thrown or rejected errors across the service boundary.
• Define the expected account-selection behavior for SIWS and signing flows when multiple wallet accounts exist.
• Decide whether secret-key hydration should be centralized and how invalid stored keys should be reported.
• Add focused tests for the agreed behavior before changing the signing/request service implementation.

Notes

This is intentionally marked blocked and needs-spec so it does not get picked up as a mechanical CodeRabbit cleanup. The current dependency PR should not keep absorbing this broader signing/request logic work.