Docs: Update stale caching example

[JacobCoffee]

I think this is a remnant of an old pattern. IIUC the snippet in the docs would no longer work.

The following is an MCVE that shows how to use a custom store using the current interfaces.

import asyncio
from litestar import Litestar, get
from litestar.config.response_cache import ResponseCacheConfig
from litestar.stores.redis import RedisStore


@get(cache=10)
async def something() -> str:
    await asyncio.sleep(1)
    return "something"


redis_store = RedisStore.with_client(url="redis://localhost", port=6379, db=0)
cache_config = ResponseCacheConfig(store="redis_backed_store")
app = Litestar(
    [something],
    stores={"redis_backed_store": redis_store},
    response_cache_config=cache_config,
)

Some may argue this is not good DX, I personally do not find this any difficult.

IOW, the following are lines of interest. The store has to be configured at the app level and the same name has to be used in ResponseCacheConfig.store. The existing snippet passes a Store instance itself, which I do not think the current interface accepts.

redis_store = RedisStore.with_client(url="redis://localhost", port=6379, db=0)
cache_config = ResponseCacheConfig(store="redis_backed_store")
app = Litestar(
    [something],
    stores={"redis_backed_store": redis_store},
    response_cache_config=cache_config,
)

Originally posted by @Alc-Alc in #3345 (comment)

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