Hello @pcaversaccio and thank you for raising that interesting point.

I realize that the
require(msg.sender == _fxChild, "unauthorized cross-chain relay");
Is in fact equivalent to the other implementation's
if (!isCrossChain(bridge)) revert NotCrossChainCall();

This makes me think we should probably not introduce a new error and do

    function processMessageFromRoot(
        uint256, /* stateId */
        address rootMessageSender,
        bytes calldata data
    ) external override nonReentrant {
        if (!_isCrossChain()) revert NotCrossChainCall();

        _sender = rootMessageSender;
        Address.functionDelegateCall(address(this), data, "crosschain execution failled");
        _sender = DEFAULT_SENDER;
    }

What do you think ?

@Amxx good point - fully agreed; will fix this now! Quick suggestion: why not include the address of the emitter in all custom errors (i.e. here). This helps end-users identify which contract was reverted with a failed transaction, which is especially useful for complex transactions involving multiple contracts? What do you think?

error SomeError(address emitter, ..., ..., ...);
emit SomeError(address(this), ..., ..., ...);

PS: Just fixed a typo in Address.functionDelegateCall(address(this), data, "cross-chain execution failed");.

I fully agree that custom errors should start with the address of the emitter.

Ok - so let's first get this PR merged (if you agree) and thereafter I will open another PR with the custom errors that include the emitter address. How would you think about creating a dedicated error interface ICrossChainErrors (instead of the current errors.sol), where we define all the custom errors used in crosschain. This design could be later extended for all the other OZ contracts (e.g. ERC20 etc.) once solc 0.8.4 is supported.

Ok - so let's first get this PR merged (if you agree) and thereafter I will open another PR with the custom errors that include the emitter address.
100% agree

How would you think about creating a dedicated error interface ICrossChainErrors (instead of the current errors.sol), where we define all the custom errors used in crosschain. This design could be later extended for all the other OZ contracts (e.g. ERC20 etc.) once solc 0.8.4 is supported.

I'm not sure, we'll have to discuss that internally.

Sure, will work on the other PR in the meantime.