[proxy] fix connect_to_compute retry handling (#12351)

# Problem

In #12335 I moved the `authenticate` method outside of the
`connect_to_compute` loop. This triggered [e2e tests to become
flaky](https://github.com/neondatabase/cloud/pull/30533). This
highlighted an edge case we forgot to consider with that change.

When we connect to compute, the compute IP might be cached. This cache
hit might however be stale. Because we can't validate the IP is
associated with a specific compute-id☨, we will succeed the
connect_to_compute operation and fail when it comes to password
authentication☨☨. Before the change, we were invalidating the cache and
triggering wake_compute if the authentication failed.

Additionally, I noticed some faulty logic I introduced 1 year ago
https://github.com/neondatabase/neon/pull/8141/files#diff-5491e3afe62d8c5c77178149c665603b29d88d3ec2e47fc1b3bb119a0a970afaL145-R147

☨ We can when we roll out TLS, as the certificate common name includes
the compute-id.

☨☨ Technically password authentication could pass for the wrong compute,
but I think this would only happen in the very very rare event that the
IP got reused **and** the compute's endpoint happened to be a
branch/replica.

# Solution

1. Fix the broken logic
2. Simplify cache invalidation (I don't know why it was so convoluted)
3. Add a loop around connect_to_compute + authenticate to re-introduce
the wake_compute invalidation we accidentally removed.

I went with this approach to try and avoid interfering with
https://github.com/neondatabase/neon/compare/main...cloneable/proxy-pglb-connect-compute-split.
The changes made in commit 3 will move into `handle_client_request` I
suspect,

proxy/src/cache/timed_lru.rs

@@ -30,7 +30,7 @@ use super::{Cache, timed_lru};
 ///
 /// * There's an API for immediate invalidation (removal) of a cache entry;
 ///   It's useful in case we know for sure that the entry is no longer correct.
-///   See [`timed_lru::LookupInfo`] & [`timed_lru::Cached`] for more information.
+///   See [`timed_lru::Cached`] for more information.
 ///
 /// * Expired entries are kept in the cache, until they are evicted by the LRU policy,
 ///   or by a successful lookup (i.e. the entry hasn't expired yet).
@@ -54,7 +54,7 @@ pub(crate) struct TimedLru<K, V> {
 impl<K: Hash + Eq, V> Cache for TimedLru<K, V> {
     type Key = K;
     type Value = V;
-    type LookupInfo<Key> = LookupInfo<Key>;
+    type LookupInfo<Key> = Key;
 
     fn invalidate(&self, info: &Self::LookupInfo<K>) {
         self.invalidate_raw(info);
@@ -87,30 +87,24 @@ impl<K: Hash + Eq, V> TimedLru<K, V> {
 
     /// Drop an entry from the cache if it's outdated.
     #[tracing::instrument(level = "debug", fields(cache = self.name), skip_all)]
-    fn invalidate_raw(&self, info: &LookupInfo<K>) {
-        let now = Instant::now();
-
+    fn invalidate_raw(&self, key: &K) {
         // Do costly things before taking the lock.
         let mut cache = self.cache.lock();
-        let raw_entry = match cache.raw_entry_mut().from_key(&info.key) {
+        let entry = match cache.raw_entry_mut().from_key(key) {
             RawEntryMut::Vacant(_) => return,
-            RawEntryMut::Occupied(x) => x,
+            RawEntryMut::Occupied(x) => x.remove(),
         };
-
-        // Remove the entry if it was created prior to lookup timestamp.
-        let entry = raw_entry.get();
-        let (created_at, expires_at) = (entry.created_at, entry.expires_at);
-        let should_remove = created_at <= info.created_at || expires_at <= now;
-
-        if should_remove {
-            raw_entry.remove();
-        }
-
         drop(cache); // drop lock before logging
+
+        let Entry {
+            created_at,
+            expires_at,
+            ..
+        } = entry;
+
         debug!(
-            created_at = format_args!("{created_at:?}"),
-            expires_at = format_args!("{expires_at:?}"),
-            entry_removed = should_remove,
+            ?created_at,
+            ?expires_at,
             "processed a cache entry invalidation event"
         );
     }
@@ -211,10 +205,10 @@ impl<K: Hash + Eq + Clone, V: Clone> TimedLru<K, V> {
     }
 
     pub(crate) fn insert_unit(&self, key: K, value: V) -> (Option<V>, Cached<&Self, ()>) {
-        let (created_at, old) = self.insert_raw(key.clone(), value);
+        let (_, old) = self.insert_raw(key.clone(), value);
 
         let cached = Cached {
-            token: Some((self, LookupInfo { created_at, key })),
+            token: Some((self, key)),
             value: (),
         };
 
@@ -229,28 +223,9 @@ impl<K: Hash + Eq, V: Clone> TimedLru<K, V> {
         K: Borrow<Q> + Clone,
         Q: Hash + Eq + ?Sized,
     {
-        self.get_raw(key, |key, entry| {
-            let info = LookupInfo {
-                created_at: entry.created_at,
-                key: key.clone(),
-            };
-
-            Cached {
-                token: Some((self, info)),
-                value: entry.value.clone(),
-            }
+        self.get_raw(key, |key, entry| Cached {
+            token: Some((self, key.clone())),
+            value: entry.value.clone(),
         })
     }
 }
-
-/// Lookup information for key invalidation.
-pub(crate) struct LookupInfo<K> {
-    /// Time of creation of a cache [`Entry`].
-    /// We use this during invalidation lookups to prevent eviction of a newer
-    /// entry sharing the same key (it might've been inserted by a different
-    /// task after we got the entry we're trying to invalidate now).
-    created_at: Instant,
-
-    /// Search by this key.
-    key: K,
-}