Unfortunately, it likely won't be possible to autoclick with CTG Plugins. But for TMT games specifically, you can usually hold down on a button to click it repeatedly. I'll do a bit of a poorly formatted mind-dump here about potential solutions, none of them entirely pretty, all of them requiring some effort.
The last time CTG Plugins was updated was 2019, so unfortunately I doubt that the extension author will be coming back to make it compatible with the way galaxy works. Because of that, the solution would have to be galaxy letting you autoclick somehow. All of these solutions involve galaxy gaining access to the game's code.
Galaxy can already communicate with the game that is being played, so in theory all that would be needed is a tiny bit of code in the game that would listen for a certain type of message from galaxy that contains arbitrary code ("click automatically for me!") and run it.
Solution 1: Host games on galaxy
This way, we'd have control over the game's code, and could insert the hypothetical listener mentioned above. However, if a game switches to being hosted on galaxy after publication, saves would be lost.
Solution 2: Proxy games on galaxy
An ugly solution. Would make loading games take longer, the proxy would have to be imperfect, and all game saves would be lost. But it would still give control over the code.
Solution 3: Have developers include a
<script> tag in their games'
This would make the functionality opt-in, but would still give control.
Solution 4: Galaxy desktop app???????
The most outlandish by far. But when you are in control of the browser, you can inject any code you want into sites.