[in_app_purchase_android] Implement `BillingClient` connection management and introduce `BillingClientManager`

[SynSzakala]

This PR adds management of BillingClient connection to Android implementation of InAppPurchase. This should fix issues caused by lost connections.

New and previously existing connection management is extracted to a new component, BillingClientManager. This component is exported in billing_client_wrappers.dart, so that it can also be used when interacting with BillingClient directly.

Fixes https://github.com/flutter/flutter/issues/110663

Migrated from flutter/plugins PR #6309

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[SynSzakala]

@gmackall, @bparrishMines re-requesting review after migrating this PR. Hope we can get this merged soon!

[SynSzakala]

Done! Also ping @stuartmorgan on this review.

[SynSzakala]

@tarrinneal I think we actually might go forward and merge this, since @stuartmorgan already gave his approval before the migration.

[bparrishMines]

This was already approved in https://github.com/flutter/plugins/pull/6309 and I was essentially giving this a secondary review. So this should be fine to submit for @tarrinneal and I.