[Chore] Enforce safe async handling in core tools (#1255)

* chore(lint): enforce no-floating-promises in core tools

* test: cover core tool promise branches

* refactor(core/tools): drop unreachable webview-post catches, make notifications non-blocking

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Co-authored-by: Roomote <roomote@roomote.dev>
Co-authored-by: Elliott de Launay <edelaunay@wealthsimple.com>