You should still be able to global chat if you hold B while the text-to-speech is speaking. I recommend turning Local Push to Talk off in game settings so you don't have to rush back into the game to hold V. You can test this in the Audio menu 'give us a sign' test and see if you've got it working. So if you want it to recognize phrases like 'give us a sign' or to use the spirit box, you have to type what you want to say, hit Enter then immediately click back into the game in order for it to recognize. You can use this to voice chat to teammates at any time, but for the game's voice recognition to actually pick up what you're saying the game window has to be in focus. Hit Enter to begin the text-to-speech then left-click to return back to the game. To use the app in-game you can just Alt-Tab to bring up the Type to Voice Chat box and it should automatically place your cursor in the box so you can begin typing.

Test the Type to Voice Chat app and see if you can hear what you've entered.

If you want to be able to hear your TTS lines out of your speakers, right click on CABLE Output > Properties > Listen tab > Check 'Listen to this device' and set to Default Playback Device. Under Recording tab make sure 'CABLE Output' is selected as Default Device. Under Playback tab set your Default sound device to whatever your normal audio output was (speakers/headphones). Now go into your Windows sound settings, Sound Control Panel (top right). Click the microphone icon to change the voice. Once both are installed and you've restarted PC, open the Type to Voice Chat app, click the speaker icon and set it to 'CABLE Input (VB-Audio Virtual Cable)'. Slightly complicated if you've never messed with virtual audio cables before, but it does work. I think this app may be the best solution though not perfect. I was looking for ways to make this game more playable for a friend who is mute.

Vb virtual audio cable preventing sleep