Support of mTLS for external URL and for internal URL in parallel

HA com app 2025.8.7
The external URL is through a mTLS cloudflare URL and it works splendid.
I am trying to set up a mTLS for my internal URL using nginx as reverse proxy on a stand alone server, using self signed certificates for the client and the server. The mTLS works OK when the internal URL for HA is accessed with chrome from my phone, it pops up a window asking to select the right client certificate as expected and it works perfect thru all the functions of HA.
However, the HA com app does not succeed to connect the mTLS internal URL as it presents its client cloudflare certicate to the nginx reverse proxy serving the internal link and not the self signed client certificate available in the certificate store of the phone. There is no window popping up to select the self signed client certificate instead of the cloudflare one.
Hence my question: is the HA com app able to manage one mtls for the external URL and another one for the internal URL and if yes how to get it to take the right certificate for the applicable URL as the HA comp app switches seemingly between external and internal URLs?
Any feedback, return of experience welcome.
Thanks

Same issue if adding a new server with mTLS access, HA comp app sends the client certificate of Cloudflare selected when setting up the 1st server via a mTLS cloudflare external link.
It look like the HA comp app is limited by design to handle a single mTLS connection.
I would expect that HA comp app would be able to manage the specific mTLS set up for each of the end points that it has to serve via external and internal url for each of its declared server.
Is it a valid expectation?
Thanks for any feedback