I remain shocked that an auth company CEO would push a solution without HttpOnly protection. This would not get by our security audits, and Auth0 and many open source tools I've used do not have the same limitation (Auth0 sets it in the SDK rather than a proxy).
OWASP and NIST are aligned that HttpOnly cookie should be used:
[1] https://cheatsheetseries.owasp.org/cheatsheets/Session_Manag...
[2] https://pages.nist.gov/800-63-3/sp800-63b.html#711-browser-c...