[management] Fix what a second review found in the credential check

Four defects and two pieces of wording, from cubic's pass over the branch.

A provider that asks the proxy to skip TLS verification was checked with a
client that verifies it, so a self-hosted endpoint behind a self-signed
certificate was refused for the one reason its operator had already declared
they accept. Those records now save unchecked, alongside the other cases this
cannot speak for. Sending the credential over a connection management declines
to verify was the other way out, and a worse one.

A key pasted with surrounding whitespace passed its check and then failed every
request: the vendor call trims before building the auth header, the synthesiser
substitutes the stored value verbatim. The key is now stored in the form it
will be sent, so what was checked is what runs.

The proxy-guard test resolved api.openai.com for real before reaching its own
transport, and on a runner with no egress that lookup failed as an
UnreachableError too — so it passed while never exercising the socket guard it
is named for.

A DNS timeout said only that the lookup failed. It now says so as a timeout,
without borrowing the wording of a connection that was never attempted.

The create description promised more than the check delivers: for Bedrock the
runtime host is resolved but never contacted, so a public host that does not
answer is still stored. It says that now, and names the TLS exemption above.
The invalid-upstream message no longer quotes the URL back, which was the one
path in this feature that echoed what the operator typed.

The live suite's single-vendor scope and its dependence on vendor availability
are now stated where the tests are, rather than left to be rediscovered.

shared/management/http/api/openapi.yml

@@ -14146,7 +14146,11 @@ paths:
       description: |
         Connects a new Agent Network AI provider for the account.
 
-        The upstream URL and credential are checked against the vendor before the provider is stored, so a record that cannot reach its vendor is refused rather than saved. Returns 422 with a message naming whichever of the two is at fault — a rejected credential, an upstream that does not resolve or answer, a vendor outage, and a timeout all block the write. Only what cannot be checked at all is exempt and stored unverified: a catalog provider with no listing endpoint, one with no host to derive a listing from, and an upstream resolving to a private address the management service will not dial.
+        The credential is checked against the vendor's model listing before the provider is stored, so a record the vendor will not accept is refused rather than saved. Returns 422 naming what is at fault — a rejected credential, a listing endpoint that does not resolve or answer, a vendor outage, and a timeout all block the write.
+
+        How much of the upstream URL that covers depends on the provider. Where the listing is served from the upstream itself, reaching it proves the URL. Where the catalog entry has a listing host of its own — Bedrock, whose listing comes from the control plane — the configured runtime host is resolved on its own account but never contacted, so a public host that does not answer is still stored.
+
+        Only what cannot be checked at all is exempt and stored unverified: a catalog provider with no listing endpoint, one with no host to derive a listing from, an upstream resolving to a private address the management service will not dial, and a provider configured to skip TLS verification.
       tags: [ Agent Network ]
       security:
         - BearerAuth: [ ]