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This is an interesting question, because, if I understand you correctly, you have a very unusual situation.
RStudio Server Pro supports integration with many different single sign-on (SSO) systems (in addition to simple password auth. Many customers use PAM (including for configuring LDAP / active directory). And where PAM is not suitable, you can configure proxied authentication.
It makes sense that you want to use SSH at the server level, but using the IDE is most likely going to require some form of integration with your in-house authentication mechanism.
I suggest that your best course of action is to contact our support team, or your RStudio customer success rep. They will be able to arrange a meeting with an RStudio solutions engineer, where we can dive deeper into your unique circumstances and recommend a way forward.