vsce package command fails with latest react components in version 18

[odockal]

Packaging extension using vsce introduces an error during build due to react-* dependencies in version 18. I am looking at changes done in #694.
Reproducer: vsce package

 ERROR  Command failed: npm list --production --parseable --depth=99999 --loglevel=error
npm ERR! code ELSPROBLEMS
npm ERR! invalid: @types/react@18.0.21 /home/odockal/git/vscode-tekton/node_modules/@types/react
npm ERR! invalid: react-dom@18.2.0 /home/odockal/git/vscode-tekton/node_modules/react-dom
npm ERR! invalid: react@18.2.0 /home/odockal/git/vscode-tekton/node_modules/react
npm ERR! missing: @babel/core@^7.0.0, required by @emotion/babel-plugin@11.10.5
npm ERR! missing: @babel/core@^7.0.0-0, required by @babel/plugin-syntax-jsx@7.18.6

npm ERR! A complete log of this run can be found in:
npm ERR!     /home/odockal/.npm/_logs/2022-11-08T10_37_59_927Z-debug.log

Error: Command failed: node_modules/.bin/vsce package --no-yarn
    at checkExecSyncError (node:child_process:826:11)
    at Object.execSync (node:child_process:900:15)
    at CodeUtil.packageExtension (/home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/util/codeUtil.js:171:23)
    at ExTester.<anonymous> (/home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/extester.js:80:27)
    at Generator.next (<anonymous>)
    at /home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/extester.js:18:71
    at new Promise (<anonymous>)
    at __awaiter (/home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/extester.js:14:12)
    at ExTester.installVsix (/home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/extester.js:61:16)
    at ExTester.<anonymous> (/home/odockal/git/vscode-tekton/node_modules/vscode-extension-tester/out/extester.js:128:24)