Do you maintain session information on the server or do you use web token and make server state-less? Why did you choose one over the other?
The way I am handling sessions is by embedding an "ephemeral session id" and a username in a web token and having that same id set as a separate cookie. When a request is received by the server then the "session id" embedded in the token is compared with the value stored in that separate cookie. If that matches then the username is extracted from the token. In response to that request, a new session id is generated and a new token is created and the value of a separate cookie is set to this new session id.
Do you see problems with this approach?
Are there better ways to handle sessions without storing state on servers?
If you are doing a MPA, I would only use a session cookie and set the secure only flag as well as the same origin flag for the cookie. Obviously any auth and session management should be done via TLS (and only allow the last few latest and greatest, don't let the client downgrade you to something that can be exploited), if they compromise TLS we all have bigger problems than the fact that they got your cookie and a user session. If the client is owned by a hack there is not much you can do, as they already have the client, you just have to protect your endpoints from that client exploiting your server for more than that users information or privileged escalation attacks.
But honestly the best thing to do, is not roll your own. Use an existing auth solution. Httpd is pretty hardened and they are plenty of auth solutions for it, if you are using it.