Gholdengo with covert cloak can only be damaged by these things:
- Regular attacks that aren't normal, fighting or poison type
- Entry hazards
- The end of turn damaging effects of trapping moves like fire spin
- Recoil damage
- Sea of fire caused by fire + grass pledge
- Any Pokemon with the abilities mold breaker, teravolt, turboblaze, neutralising gas or Mycelium might can bypass gholdengo's ability to damage it with the status moves that Good as Gold protects from.
- Contact effects like Flame body, Iron barbs, Rough skin, Rocky helmet, Spiky shield, Aftermath, Effect spore, Burning bulwark
- Jacoba and Rowap berry
- Bad Dreams
- If gholdengo terastralises, then it can become a type vulnerable to being poisoned by toxic spikes or damaged by/immune to different things depending on the type, like sandstorm or poison point.
- Confusion
Hail was replaced by snow in scarlet and violet but if it was in the game then gholdengo would be damaged by it.
I don't think Synchronise will be able to burn/poison gholdengo because gholdengo doesn't learn any moves that can inflict those statuses.
Normally soak wouldn't work on gholdengo because it is a status move which Good as Gold makes it immune to.
Hope this helps, let me know if I missed anything.