Bidirectional TVS supressor instead of Snubber for Triac
TVS Diode 1,5KE250CA

The TVS Diode type 1,5KE250CA has a breakdown voltage of between 237 volts and 263 volts. This isn't an RMS rating; it's a peak voltage rating - take note.

Voltage (Load) 230 VAC

220 volts (diagram) or maybe you mean 230 volts as per the above statement has a peak voltage of \$\sqrt2\times 230\$ = 325 volts and will instantly fry the TVS you chose. The TVS will clamp somewhere between a peak voltage of 263 volts and 344 volts and you cannot determine where this will happen so, no that TVS isn't suitable.
And, unfortunately, none of the TVS diodes in the data sheet will really be any good for you because most countries will have specifications on indirect lightning surge protection for households of around the 1500 peak volt limit so, it's unlikely that any TVS is going to be able to be used at all effectively.

Therefore I would like to know if it possible to use a bidirectional
TVS Diode instead of a snubber and if it still offers enough
protection.

No, it won't be at all suitable - stick with snubbers - they don't hard clamp and therefore they won't try to take a massive current peak should indirect lightning surges affect your neighbourhood.