fix: Resolve no-floating-promises lint errors (#12196)

* fix: Resolve no-floating-promises lint errors

Adds await or void to 10 unhandled promises. Notable fixes: a test
assertion using `.resolves` was never awaited, and a custom emoji
fetch with setState was running during render instead of in an effect.

* chore: Promote no-floating-promises to error

Now that all occurrences are fixed, prevent regressions.

.oxlintrc.json

@@ -87,6 +87,7 @@
         "import/no-named-as-default": "off",
         "import/no-named-as-default-member": "off",
         "typescript/consistent-type-imports": "error",
+        "typescript/no-floating-promises": "error",
         "no-unused-vars": [
           "error",
           {