First of all, let me clarify that this website just collects the sentiment of miners—it is in no way binding for the actual activation for which code isn't even proposed.
Assuming that Taproot will use BIP8 as its activation mechanism, there is only one state in which miners are required to signal. Mining is mandatory in the last difficulty epoch of the signaling period, but only if the activation proposal is using
In any other circumstances, all miners can freely choose whether to signal readiness. Also, it is not expected that the block version will get updated with Taproot, blocks would only be different in that they include transactions using taproot.
Once the proposal is active, miners are free to include transactions that spend v1 segwit outputs, but they are not required to do so. As always, miners may freely select which valid transactions to include in their blocks. A miner may decide not to include Taproot transactions without any repercussions. Presumably, the next miner that supports Taproot would include such transactions if they are among the transactions with the highest feerates.
For example, a miner that didn't update their fullnode since the Taproot code got added would consider Taproot transactions non-standard. Since nodes don't include non-standard transactions in block templates, the miner would still be able to build blocks that are valid to the network, simply by not including Taproot transactions.