bug: Kill() invoked shortly after Run() results in data races

[lrstanley]

Describe the bug
If you invoke Kill, shortly after invoking Run, it results in data races (shown below), in addition to some cases of fatal error: sync: unlock of unlocked mutex (couldn't reliably replicate). This could occur in a few scenarios, some examples:

• Short-duration tests, where a program is spun up and shut down very quickly (using Kill to ensure cleanup, where sending Quit doesn't necessarily guarantee this).
• Program's spun up from potentially remote connections, where someone could theoretically introduce a lot of connections that terminate quickly.

Setup
Please complete the following information along with version numbers, if applicable.

• OS: n/a
• Shell: n/a
• Terminal Emulator: n/a
• Terminal Multiplexer: n/a

To Reproduce
The following test reproduces:

func TestKillDuringStartupRace(t *testing.T) {
	for range 100 {
		p := NewProgram(&testModel{},
			WithInput(bytes.NewBuffer(nil)),
			WithOutput(io.Discard),
			WithoutSignals(),
		)

		done := make(chan struct{})
		go func() {
			_, _ = p.Run()
			close(done)
		}()

		p.Kill()

		select {
		case <-done:
		case <-time.After(time.Second):
			t.Fatal("program did not stop")
		}
	}
}

Expected behavior

Due to Run not really providing a way to know when things are "started enough", it's hard to know when or when not Kill should be safe to invoke. I would expect one of these two:

1. Provide a way to know when it's safe to invoke Kill.
2. Make Kill block until startup is safe enough to easily be cancelled/"unrolled". However, this still needs to ensure that it can't run into a scenario where it blocks forever.

Additional context

go test running with -race, showing the data race

$ go test -race -timeout 20s -count 20 -cpu 1,4 -run 'TestKillDuringStartupRace$' .
==================
WARNING: DATA RACE
Write at 0x00c0000b47b0 by goroutine 10:
  charm.land/bubbletea/v2.(*Program).Run()
      /home/liam/tmp/fork-bubbletea/tea.go:997 +0x87
  charm.land/bubbletea/v2.TestKillDuringStartupRace.func1()
      /home/liam/tmp/fork-bubbletea/tea_test.go:230 +0x33

Previous read at 0x00c0000b47b0 by goroutine 9:
  charm.land/bubbletea/v2.(*channelHandlers).shutdown()
      /home/liam/tmp/fork-bubbletea/tea.go:415 +0xd2
  charm.land/bubbletea/v2.TestKillDuringStartupRace.(*Program).Kill.(*Program).shutdown.func5()
      /home/liam/tmp/fork-bubbletea/tea.go:1246 +0x58
  sync.(*Once).doSlow()
      /usr/local/go/src/sync/once.go:78 +0xa1
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 10 (running) created at:
  charm.land/bubbletea/v2.TestKillDuringStartupRace()
      /home/liam/tmp/fork-bubbletea/tea_test.go:229 +0x359
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 9 (running) created at:
  testing.(*T).Run()
      /usr/local/go/src/testing/testing.go:2101 +0xb12
  testing.runTests.func1()
      /usr/local/go/src/testing/testing.go:2585 +0x85
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.runTests()
      /usr/local/go/src/testing/testing.go:2583 +0x9e9
  testing.(*M).Run()
      /usr/local/go/src/testing/testing.go:2443 +0xf4b
  main.main()
      _testmain.go:102 +0x164
==================
==================
WARNING: DATA RACE
Write at 0x00c0000b4888 by goroutine 10:
  charm.land/bubbletea/v2.(*Program).Run()
      /home/liam/tmp/fork-bubbletea/tea.go:1077 +0xc24
  charm.land/bubbletea/v2.TestKillDuringStartupRace.func1()
      /home/liam/tmp/fork-bubbletea/tea_test.go:230 +0x33

Previous read at 0x00c0000b4888 by goroutine 9:
  charm.land/bubbletea/v2.TestKillDuringStartupRace.(*Program).Kill.(*Program).shutdown.func5()
      /home/liam/tmp/fork-bubbletea/tea.go:1259 +0xf1
  sync.(*Once).doSlow()
      /usr/local/go/src/sync/once.go:78 +0xa1
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 10 (running) created at:
  charm.land/bubbletea/v2.TestKillDuringStartupRace()
      /home/liam/tmp/fork-bubbletea/tea_test.go:229 +0x359
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 9 (running) created at:
  testing.(*T).Run()
      /usr/local/go/src/testing/testing.go:2101 +0xb12
  testing.runTests.func1()
      /usr/local/go/src/testing/testing.go:2585 +0x85
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.runTests()
      /usr/local/go/src/testing/testing.go:2583 +0x9e9
  testing.(*M).Run()
      /usr/local/go/src/testing/testing.go:2443 +0xf4b
  main.main()
      _testmain.go:102 +0x164
==================
==================
WARNING: DATA RACE
Write at 0x00c0000b48e8 by goroutine 10:
  charm.land/bubbletea/v2.(*Program).initInputReader()
      /home/liam/tmp/fork-bubbletea/tty.go:69 +0x22c
  charm.land/bubbletea/v2.(*Program).Run()
      /home/liam/tmp/fork-bubbletea/tea.go:1101 +0x11a9
  charm.land/bubbletea/v2.TestKillDuringStartupRace.func1()
      /home/liam/tmp/fork-bubbletea/tea_test.go:230 +0x33

Previous read at 0x00c0000b48e8 by goroutine 9:
  charm.land/bubbletea/v2.TestKillDuringStartupRace.(*Program).Kill.(*Program).shutdown.func5()
      /home/liam/tmp/fork-bubbletea/tea.go:1249 +0x6d
  sync.(*Once).doSlow()
      /usr/local/go/src/sync/once.go:78 +0xa1
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 10 (running) created at:
  charm.land/bubbletea/v2.TestKillDuringStartupRace()
      /home/liam/tmp/fork-bubbletea/tea_test.go:229 +0x359
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.(*T).Run.gowrap1()
      /usr/local/go/src/testing/testing.go:2101 +0x38

Goroutine 9 (running) created at:
  testing.(*T).Run()
      /usr/local/go/src/testing/testing.go:2101 +0xb12
  testing.runTests.func1()
      /usr/local/go/src/testing/testing.go:2585 +0x85
  testing.tRunner()
      /usr/local/go/src/testing/testing.go:2036 +0x21c
  testing.runTests()
      /usr/local/go/src/testing/testing.go:2583 +0x9e9
  testing.(*M).Run()
      /usr/local/go/src/testing/testing.go:2443 +0xf4b
  main.main()
      _testmain.go:102 +0x164
==================
--- FAIL: TestKillDuringStartupRace (0.08s)
    testing.go:1712: race detected during execution of test
FAIL
FAIL    charm.land/bubbletea/v2 12.195s
FAIL