[extensionauth] Remove deprecated methods (#12547)

<!--Ex. Fixing a bug - Describe the bug and how this fixes the issue.
Ex. Adding a feature - Explain what this achieves.-->
#### Description

Follows #12480

Author: mx-psi

.chloggen/mx-psi_remove-deprecated-methods.yaml

@@ -0,0 +1,25 @@
+# Use this changelog template to create an entry for release notes.
+
+# One of 'breaking', 'deprecation', 'new_component', 'enhancement', 'bug_fix'
+change_type: breaking
+
+# The name of the component, or a single word describing the area of concern, (e.g. otlpreceiver)
+component: extensionauth
+
+# A brief description of the change.  Surround your text with quotes ("") if it needs to start with a backtick (`).
+note: Remove deprecated methods from the `Func` types.
+
+# One or more tracking issues or pull requests related to the change
+issues: [12547]
+
+# (Optional) One or more lines of additional information to render under the primary note.
+# These lines will be padded with 2 spaces and then inserted directly into the document.
+# Use pipe (|) for multiline entries.
+subtext:
+
+# Optional: The change log or logs in which this entry should be included.
+# e.g. '[user]' or '[user, api]'
+# Include 'user' if the change is relevant to end users.
+# Include 'api' if there is a change to a library API.
+# Default: '[user]'
+change_logs: [api]

extension/extensionauth/client.go

@@ -39,25 +39,9 @@ func (of clientOptionFunc) apply(e *defaultClient) {
 // ClientRoundTripperFunc specifies the function that returns a RoundTripper that can be used to authenticate HTTP requests.
 type ClientRoundTripperFunc func(base http.RoundTripper) (http.RoundTripper, error)
 
-// Deprecated: [v0.121.0] No longer used, will be removed.
-func (f ClientRoundTripperFunc) RoundTripper(base http.RoundTripper) (http.RoundTripper, error) {
-	if f == nil {
-		return base, nil
-	}
-	return f(base)
-}
-
 // ClientPerRPCCredentialsFunc specifies the function that returns a PerRPCCredentials that can be used to authenticate gRPC requests.
 type ClientPerRPCCredentialsFunc func() (credentials.PerRPCCredentials, error)
 
-// Deprecated: [v0.121.0] No longer used, will be removed.
-func (f ClientPerRPCCredentialsFunc) PerRPCCredentials() (credentials.PerRPCCredentials, error) {
-	if f == nil {
-		return nil, nil
-	}
-	return f()
-}
-
 var _ Client = (*defaultClient)(nil)
 
 type defaultClient struct {