I’ve succesfully connected Google Assistent to SmartThings but when I press the + (In ST) and press Voice Assistent I can see the Google Assistent option but I can’t click it?
You can add your devices to Google Assistant/Home, not the other way around. You cannot add Google Home devices to your ST configuration.
If you want to do something like that, use Google Assistant Relay, but it is not really the same thing what you are looking for.
You can’t let your Google Home say something if (for example) your lamp is still on? Or do you know some cheap speakers that work with ST?
By default, unfortunately not. If you have a computer running 24/7 then try Google Assistant Relay (search the forum for it). Install it, and use it together with Web Core.
Cheap speaker? Maybe some cheap Sonos speakers, the IKEA ones are quite cheap, but still 100 EUR/GBP/USD at least…