SAML is not compatible with MSAL. MSAL uses OIDC.
There is no SAML client-side stack for JS.
I assume that you are using Entra ID as your IDP?
I'm unsure what you mean by "application that wants access to this app"?
Your MSAL app. accesses Entra ID. Your SAML app. accesses Entra ID.
The apps can't access each other?