[11.x] Fix database reconnecting logic

[stancl]

Fixes #53692.

Sending this as a draft for convenience so that this can move forward once I get confirmation that my idea of the fix is correct.

Before this is merged, a test should be added verifying that connections are now repaired by the reconnect() call.

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[stancl]

The only tests that seem to relate to the reconnecting logic are in DatabaseConnectionTest and all seem to have transaction-specific logic. Additionally, custom reconnectors are set for the created connections and pretty much everything in that test case uses mocks.

To test that the default reconnector re-creates the connection in DatabaseManager as well as heals the Connection itself, I think avoiding mocks would be preferable but I'm not sure how you tend to test these sorts of things.

The test I'd like to add would be essentially something like this (just copied this from a codebase where I'm using Pest):

config(['database.connections.testbench' => [
    'driver' => 'mysql',
    'host' => '127.0.0.1',
    'username' => 'root',
    'password' => 'invalid-credentials',
    'database' => 'forge',
    'prefix' => '',
]]);

$connection = DB::connection('testbench');

expect($connection->getRawPdo())->not()->toBeNull();

DB::purge('testbench');

expect($connection->getRawPdo())->toBeNull();

// normally triggered by a query but we're not establishing a connection to a real server here
$connection->reconnectIfMissingConnection();

// fails if I revert my patch
expect($connection->getRawPdo())->not()->toBeNull();

DB::purge('testbench');

[stancl]

Marking as ready for review, please let me know how I should add the test or feel free to just push it.

[stancl]

@taylorotwell Do you want to add the regression test in some form?