[build] Remove nofixdeps for grpc_base (grpc#31148)

BUILD

@@ -3365,12 +3365,10 @@ grpc_cc_library(
         "absl/functional:function_ref",
         "absl/memory",
         "absl/meta:type_traits",
-        "absl/random",
         "absl/status",
         "absl/status:statusor",
         "absl/strings",
         "absl/strings:str_format",
-        "absl/synchronization",
         "absl/time",
         "absl/types:optional",
         "absl/types:variant",
@@ -3379,7 +3377,6 @@ grpc_cc_library(
     ],
     language = "c++",
     public_hdrs = GRPC_PUBLIC_HDRS + GRPC_PUBLIC_EVENT_ENGINE_HDRS,
-    tags = ["nofixdeps"],
     visibility = ["@grpc:alt_grpc_base_legacy"],
     deps = [
         "activity",
@@ -3403,7 +3400,6 @@ grpc_cc_library(
         "default_event_engine",
         "dual_ref_counted",
         "error",
-        "event_engine_common",
         "event_log",
         "exec_ctx",
         "experiments",
@@ -3415,7 +3411,6 @@ grpc_cc_library(
         "grpc_public_hdrs",
         "grpc_sockaddr",
         "grpc_trace",
-        "handshaker_registry",
         "http2_errors",
         "init_internally",
         "iomgr_fwd",
@@ -3440,7 +3435,6 @@ grpc_cc_library(
         "slice_refcount",
         "sockaddr_utils",
         "status_helper",
-        "table",
         "thread_quota",
         "time",
         "transport_fwd",