Use client logger in more places (core code) (#4899)

* Use client logger for sync

Use the logger attached to the MatrixClient when writing log messages out of
the sync api. This helps figure out what's going on when multiple clients are
running in the same JS environment.

* Use client logger for to-device message queue

* Use client logger in `PushProcessor.rewriteDefaultRules`

* use client logger in `ServerCapabilities`

* Mark global `logger` as deprecated

spec/unit/pushprocessor.spec.ts

@@ -28,6 +28,7 @@ import {
     TweakName,
 } from "../../src";
 import { mockClientMethodsUser } from "../test-utils/client";
+import { logger } from "../../src/logger.ts";
 
 const msc3914RoomCallRule: IPushRule = {
     rule_id: ".org.matrix.msc3914.rule.room.call",
@@ -209,7 +210,7 @@ describe("NotificationService", function () {
                 msgtype: "m.text",
             },
         });
-        matrixClient.pushRules = PushProcessor.rewriteDefaultRules(matrixClient.pushRules!);
+        matrixClient.pushRules = PushProcessor.rewriteDefaultRules(logger, matrixClient.pushRules!);
         pushProcessor = new PushProcessor(matrixClient);
     });
 
@@ -731,7 +732,7 @@ describe("Test PushProcessor.partsForDottedKey", function () {
 
 describe("rewriteDefaultRules", () => {
     it("should add default rules in the correct order", () => {
-        const pushRules = PushProcessor.rewriteDefaultRules({
+        const pushRules = PushProcessor.rewriteDefaultRules(logger, {
             device: {},
             global: {
                 content: [],
@@ -867,7 +868,7 @@ describe("rewriteDefaultRules", () => {
     });
 
     it("should add missing msc3914 rule in correct place", () => {
-        const pushRules = PushProcessor.rewriteDefaultRules({
+        const pushRules = PushProcessor.rewriteDefaultRules(logger, {
             device: {},
             global: {
                 // Sample push rules from a Synapse user.