Feature Request: Add Bitcoin RPC connection validation in Admin Guardian Setup

[hensg]

Add a test connection validation for the Bitcoin RPC during the Admin Guardian Setup [1], similar to the functionality provided by Sparrow [2]. This feature would ensure that the Bitcoin RPC is configured correctly, preventing common mistakes like incorrect RPC addresses or missing passwords.

Without this validation, users might accidentally generate an invalid bitcoin RPC address in local.json, causing the Fedimint service to fail to start. The user would then need to manually edit the local.json to fix the issue, which could be error-prone and time-consuming.

1. Admin Guardian Setup
   

2. Sparrow Bitcoin RPC configuration
   

[Kodylow]

We talked about this previously and this needs to be implemented fedimint side not ui side, but agree we need it @dpc

[Kodylow]

I also can't do this in the browser because of CORs, so has to be backend

[elsirion]

fedimint/fedimint#5968