Will stakers sell ETH immediately after unlocking?

Maybe, but there are still limitations. There is a withdrawal/deposit queue that limits how fast people can stake and unstake. This is again a mechanism to keep the chain stable, and will not let the rapid fluctuations of the Ethereum application layer affect the security of the chain.

The deposit/withdrawal bottleneck is limited to X/ETH per day, where X is equal to:

Number of validators / 65536, rounded down to the nearest integer.

The number 65536 is 2 raised to the 16th power. For some reason, Ethereum developers love these square numbers. It's called the Churn Limit Quotient, and you can read about it here and here.

Currently, there are 433,916 Ethereum validators on the Beacon Chain. To find how many validators per epoch, divide it by 65,536 and round down to the nearest integer.

433,916 (total validators) / 65,536 6 validators per epoch

So the activation/deactivation count is 6 validators per epoch. An Ethereum epoch is 6.4 minutes, 225 epochs in 24 hours.

Therefore, the current rate of validator activation/deactivation is 1,350 per day.