[2.7] Composition API's inject doesn't work for things provided in the same component

[maxbogue]

Version

2.7.14

Reproduction link

codesandbox.io

Steps to reproduce

Using the Composition API, provide a value and then inject it in the same component.

What is expected?

The value will be injected; this is the behavior in the 2.6 @vue/composition-api plugin.

What is actually happening?

This injection key is not found, printing a warning (and breaking the app if it depends on this behavior):

[Vue warn]: injection "Symbol(FooKey)" not found.

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It seems this was reported before in https://github.com/vuejs/vue/issues/12636 but the fix targeted some lifecycle thing instead of this underlying functionality change. I'm trying to upgrade my company from Vue 2.6 to Vue 2.7 (and hopefully to Vue 3 after that) but little breaking changes like this are making it very difficult.