Most gamers and streamers capture and record one video at a time. For a more complex setup, you are going to need a capture card that can handle it. The ezcap Dual 4K HDMI Video Capture Card is worth a look. It has a USB 3.1 interface and supports 4k30 and 1080p60 captures and streams. It has a plug & play design and works with Windows, macOS, and Linux.
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You can use the ezcap365 Dual CamLink RAW PCIe capture card for streaming and recording. You can find two x HDMI and 2 audio ports on it. You can control the inputs independently.
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