A good question and I think @JDRoberts has it right. Matter does bring some of HomeKit’s benefits on security & local control, but it’s not expected to be the same degree and adherence.
HomeKit has its security, while Matter has publicly confirmed a few details, e.g., AES-128.
On local control, apparently Matter supports {and thus not require?} a “fully local” smart home, though I hope to see more clarity soon. Project CHIP’s April 2021 presentation seems to also imply local-first with the line “extensible to the cloud” (e.g., Matter is only a device-to-device protocol),
So, IoT devices can make their own cloud connections or seemingly piggyback their connection to Wi-Fi internet router to exit the Matter LAN → communicate with the cloud.
The “fully local” quote from Eve Systems,
McIrvin said Wyze is also waiting to see how the specification handles local control of devices, which is important for Wyze customers. CHIP does show local communications and control of devices using Thread and a controller, while also allowing communication back to the cloud if the manufacturer wants to connect its device to an app or another service.
Eve Systems, a maker of HomeKit-certified sensors and other devices, is enthusiastic about how CHIP enables local control and the chance to preserve users’ privacy. As Tim Both, a brand manager at Eve Systems, wrote to me in an email:
Our core reason for exclusively supporting HomeKit is the strong, privacy-honoring, internet-independent platform approach…Having data to be required by design to pass through multiple clouds before successfully executing a command was never an option for us. Project CHIP not only supports a fully local, secure and private smart home but it really takes it to the next level. And as other platform members beyond Apple are part of the initiative, that will surely lead to exciting new possibilities for consumers that aren’t currently rooted in the world of Apple devices. And through our involvement with Project CHIP, we’re of course actively working on bringing Eve to those consumers, as well.
EDIT, a neat slide from the Thread Group’s April 2020 presentation on Project CHIP,

One of the key goals of Project CHIP is bringing together the best of what the ZigBee Alliance offers in dotdot, what Google has delivered with Weave, and what Apple has delivered in HomeKit. And to converge these into a singular consumer-focused, or at least initially consumer-focused, IoT application layer for the home. Which is Project CHIP.
So I’d interpreted it as borrowing & creating a new standard, but “converging” is an interesting word.