Work around DT conflict; bump TS and @types/styled-components (#5586)

@types/styled-components causes a conflict with @types/react-native. See DefinitelyTyped/DefinitelyTyped#33311.

Close #5294

Co-authored-by: repo-ranger[bot] <39074581+repo-ranger[bot]@users.noreply.github.com>

package.json

@@ -97,7 +97,8 @@
     "check-types:package": "tsd badge-maker",
     "check-types:frontend": "tsc --noEmit --project .",
     "depcheck": "check-node-version --node \">= 12.0\"",
-    "postinstall": "run-s --silent depcheck",
+    "fix-issue-5294": "rimraf node_modules/@types/react-native",
+    "postinstall": "run-s --silent depcheck fix-issue-5294",
     "prebuild": "run-s --silent depcheck",
     "features": "node scripts/export-supported-features-cli.js > supported-features.json",
     "defs": "node scripts/export-service-definitions-cli.js > service-definitions.yml",
@@ -155,7 +156,7 @@
     "@types/react-helmet": "^6.1.0",
     "@types/react-modal": "^3.10.6",
     "@types/react-select": "^3.0.19",
-    "@types/styled-components": "4.1.8",
+    "@types/styled-components": "5.1.3",
     "@typescript-eslint/eslint-plugin": "^2.34.0",
     "@typescript-eslint/parser": "^2.34.0",
     "babel-plugin-inline-react-svg": "^1.1.1",
@@ -247,7 +248,7 @@
     "tmp": "0.2.1",
     "tsd": "^0.13.1",
     "ts-mocha": "^7.0.0",
-    "typescript": "^3.8.3"
+    "typescript": "^4.0.3"
   },
   "engines": {
     "node": "^12.18.3",