GSS isn't under Cloud and doesn't have the same deprecation policy. Cloud explicitly states that it has a minimum 1-year turndown on any feature they disable.
Site Search seems like an infra offering to me.
Not an expert by any means but I would put more weight to Google's ONE year promise over (to give an example) HPE's twenty years promise. I know it is a cheap shot because I am pretty sure HPE will be bought and sold at least once in the next twenty years.
We were users of the Google Mini Search appliance, went to a 3rd party in-house installed search solution that we did not like and then a year ago went to GSS. We are looking again for something suitable. The best part of the Google Site Search was search fidelity.