`OAuthClientInformationFull.redirect_uris`: pydantic strict-type-equality breaks `AnyUrl(x) != AnyHttpUrl(x)` round-trip

Summary
When implementing a custom OAuth provider against the MCP Python SDK, callers must construct OAuthClientInformationFull instances. The SDK declares redirect_uris: list[AnyUrl] (where AnyUrl is pydantic's base URL type). Passing pydantic's stricter subtype AnyHttpUrl (or any other AnyUrl subtype) causes silent equality failures downstream: AnyUrl("https://...") == AnyHttpUrl("https://...") returns False in pydantic v2, even when the two URLs serialize identically. This breaks redirect_uri matching during the /authorize → /token exchange.
Reproducer

from pydantic import AnyUrl, AnyHttpUrl
from mcp.server.auth.provider import OAuthClientInformationFull

# pydantic v2 strict-type equality
u1 = AnyUrl("https://example.com/callback")
u2 = AnyHttpUrl("https://example.com/callback")
assert str(u1) == str(u2)   # True (both render the same)
assert u1 == u2              # FAILS in pydantic v2 — different runtime types

# Concrete impact in OAuth flow:
client_info = OAuthClientInformationFull(
    client_id="test",
    redirect_uris=[AnyHttpUrl("https://example.com/cb")],
    # ...other required fields
)
# When the /authorize request arrives with redirect_uri parameter, the SDK
# constructs an AnyUrl from the query string and checks membership:
incoming = AnyUrl("https://example.com/cb")
assert incoming in client_info.redirect_uris   # FAILS — type mismatch

Expected behavior
OAuthClientInformationFull.redirect_uris should accept and compare-equal across AnyUrl and AnyUrl subtypes (AnyHttpUrl, AnyHttpsUrl, etc.) when the underlying URL is identical.
Actual behavior
Strict-type equality causes the membership check to fail. The OAuth flow returns a generic redirect-mismatch error to the client; the underlying cause (type vs URL mismatch) is invisible without instrumenting the SDK.
Suggested fix
Two options:
Coerce on assignment. Have OAuthClientInformationFull.redirect_uris field validator coerce all values to AnyUrl (the declared base type), regardless of what the caller passes. This is the cleanest fix and matches the field declaration.
Compare-by-string. Override __eq__ on the AnyUrl chain to compare-by-str() rather than by runtime type. Broader-impact change; probably not desirable.
Option 1 is preferred. A short field_validator with mode="before" converting to AnyUrl strings before pydantic instantiates would do it.
Workaround (current PolyBot mitigation)
Pass redirect_uris as raw list[str]; pydantic coerces to AnyUrl per the field declaration. This avoids the type mismatch:

client_info = OAuthClientInformationFull(
    client_id="test",
    redirect_uris=["https://example.com/cb"],   # raw strings, not AnyHttpUrl
    # ...
)

Works at runtime; loses some IDE type hints in the caller code.
Environment
mcp Python SDK version: 1.27.1
pydantic version: 2.x
Python: 3.11+
Related code locations
In the MCP SDK:
mcp/server/auth/provider.py — OAuthClientInformationFull definition with redirect_uris: list[AnyUrl]
mcp/server/auth/handlers/authorize.py — where the membership check happens
Severity
Medium — silently breaks OAuth flows in custom-provider setups; reproducer is simple; workaround is trivial once known but the failure mode is hard to diagnose from the user-facing error.

Commencez dans mcp/server/auth/provider.py sur OAuthClientInformationFull et suivez la validation de redirect_uris, puis examinez le contrôle d’appartenance dans mcp/server/auth/handlers/authorize.py. Reproduisez l’incompatibilité AnyUrl/AnyHttpUrl avec l’exemple de l’issue et ajoutez une couverture de régression pour les entrées de sous-types. Le travail est terminé lorsque des URL équivalentes sont comparées avec succès pendant le flux authorize-to-token sans exiger que les appelants transmettent des chaînes brutes.