Fix some straightforward PhanUndeclared issues (#37201)

Mostly it's adding suppressions for false positives, and a few phpdoc
updates, `@phan-var` type assertions, and test updates.

There are some functional changes though:

* packages/forms: Add a missing `use Jetpack_Options`.
* packages/identity-crisis: Add missing `use` of some Connection
  classes.
* packages/jetpack-mu-wpcom: Remove some references to wpcom stuff that
  was removed from wpcom itself a year+ ago.
* packages/my-jetpack: Define `module_name` property on `Hybrid_Product`
  (defaulting to null). Then replace some `empty()` checks with boolean
  checks.
* packages/plans: Add missing `use Store_Product_List`.
* packages/search: Deprecate `Search_Widget->jetpack_search` prop that
  has never been set since the package was created.
* packages/sync: Fix `Replicastore::get_user()` to actually work.

I left Jetpack for a separate PR, it looks to have a long list of fixes
being needed.

I also left CRM, WP Super Cache, and VaultPress alone for now thanks to
all the phpcs exclusions that will probably make any fixes have to go
down a rabbit hole of dealing with phpcs-changed.

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/8941347348

Upstream-Ref: Automattic/jetpack@832a6a5

vendor/composer/installed.json

@@ -7,7 +7,7 @@
             "dist": {
                 "type": "path",
                 "url": "/tmp/jetpack-build/Automattic/jetpack-device-detection",
-                "reference": "b485357f23dfbb1fde3ca2db58d208e749e81e81"
+                "reference": "7313b343467ab99cef2ad495c14a546e692399ba"
             },
             "require": {
                 "php": ">=7.0"

vendor/composer/installed.php

@@ -13,7 +13,7 @@
         'automattic/jetpack-device-detection' => array(
             'pretty_version' => '2.1.3',
             'version' => '2.1.3.0',
-            'reference' => 'b485357f23dfbb1fde3ca2db58d208e749e81e81',
+            'reference' => '7313b343467ab99cef2ad495c14a546e692399ba',
             'type' => 'jetpack-library',
             'install_path' => __DIR__ . '/../automattic/jetpack-device-detection',
             'aliases' => array(),