PROBLEM
You have a blocking issue with the authentication system, or with usability or getting security to an acceptable level. In your case there is no PKCE support.
PROXYING SOLUTION
Use oidc-client which will add PKCE parameters and your SPA security supports the latest standards.
The client secret will come into play during the authorization code grant and refresh token grant messages.
Messages can be adapted server side to remove PKCE and use a client secret instead. It is quite a complex solution though and not everyone will like it.
It requires a SameSite cookie issued by the web domain. In my case I used an AWS lambda edge function that runs within a CloudFront content delivery network.
WHY DO IT THIS WAY?
In order to fit into an SPA architecture and meet wider goals in areas such as usability, coding model, mobile integration and global web performance. Depends if you feel it is worth the effort.
LINKS