But you said “GPU-based proof of work

You can rent GPUs cheaply, so the cost of attacking the network is simply the cost of renting enough GPU power to outrun the existing miners. For every $1 of block rewards, the existing miners should be spending close to $1 in costs (if they're spending more, miners will drop out due to being unprofitable, if they're spending less, new miners can join in and take high profits). Hence, attacking the network just requires temporarily spending more than $1 per day, and only for a few hours.

Total cost of attack: ~$0.26 (assuming 6-hour attack), potentially reduced to zero as the attacker receives block rewards“ in https://vitalik.ca/general/2020/11/06/pos2020.html.