[Request] Ability to deploy on paths other than the root `/`

### Describe the feature

- https://github.com/cryostatio/cryostat-legacy/issues/1810
- https://github.com/cryostatio/cryostat-legacy/issues/1860

It should be possible to deploy Cryostat behind a proxy or behind a router that places it at a path other than `/`. For example, deploying Cryostat at `http://myproject.example.com/cryostat` should work normally - visiting that URL should bring up the web client UI with all normal functionality. Requests like `GET http://myproject.example.com/cryostat/api/v3/targets` should respond as normal.

This probably involves setting the [`root-path`](https://quarkus.io/guides/http-reference#context-path) and ensuring that any links that Cryostat creates referring back to itself (ex. redirect responses) take this into account and/or use relative paths.

### Anything other information?

_No response_

Start by reviewing the two linked legacy issues and Quarkus's root-path/context-path guidance. Trace the web client, API requests, and self-referential links or redirects to identify path assumptions. Done means Cryostat deployed at /cryostat serves the UI normally and requests such as /cryostat/api/v3/targets work as expected.

Written by the indexing model from the issue text.