[v17] fixed db session page refresh and dev server terminal issues (#63644)

[nibrasohin]

backport #63644

What Changed

Fixed Two related issues with database sessions in the Web UI:

1. Page refresh shows empty page: After connecting to a database, the URL changed to /web/cluster/<cluster>/console/db/session/new, which lost the database name. Refreshing the page resulted in an empty screen because:

   • The URL no longer contained the database service name
   • Fix: The URL change to a session route was unnecessary and caused the page refresh bug so removed it

2. Dev server terminal broken: Database connections on the Vite dev server (port 3000) showed a blank terminal with no PostgreSQL prompt, while connections through the Teleport proxy (port 3080) worked correctly. This was due to a missing WebSocket proxy configuration.

   • Fix: The Vite dev server proxy configuration had rules for SSH (/connect) and Kubernetes (/kube/exec) WebSocket connections, but was missing the database exec endpoint (/db/exec) so added that.

Manual Testing

• Validated in branch/v18 that after connecting to a db from the web-ui and refreshing page lands them back on the connect dialog box.

Issue

#63014

Changelog

changelog: Fixed db session page refresh redirecting to empty page