Can I attach two external 4k monitors to an M1 macbook pro 13?

<< The BenQ plugs into a StarTech USB3 to HDMI adapter. >>

StarTech 'USB 3.0 to HDMI adapter' is a DisplayLink adapter, max resolution 2048 by 1152. [There are also several other model with slightly different names that support higher resolutions and different outputs.]

That is what got you a second, not-hardware-accelerated display.

To get it working again, install the updated DisplayLink software from StarLink, or from DisplayLink.

A M1 MacBook Pro supports one external display.

"Simultaneously supports full native resolution on the built-in display at millions of colors and: 

• One external display with up to 6K resolution at 60Hz"

MacBook Pro (13-inch, M1, 2020) - Technical Specifications

DisplayLink technology creates a "fake" display buffer in RAM, sends the data out over a slower interface to a stunt box with DisplayLink custom chips that put that data back onto a "legacy" interface. It is not a true "accelerated" display, and it can suffer from lagging. Just adding the DisplayLink Driver is not adequate to get a picture -- you need a DisplayLink "stunt-box" or a Dock that includes DisplayLink chips.

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It may be acceptable for a second display showing slow-to-change data such as computer program listings, stock quotes, or spreadsheets, but NOT for full motion Video, not for Video editing, and absolutely not for gaming. Mouse-tracking on that display can lag, and can make you feel queasy.

In a pinch, it may even play Internet videos (as one user put it) “without too many dropped frames".

This is in stark contrast to the Apple standard for its built-in hardware-accelerated displays, which are suitable for production/display of cinema-quality video with NO dropped frames, and NO dropouts or partial-blank scan lines due to memory under-runs or other issues.

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It is really nice to know that you can use a DisplayLink display if you MUST have an additional display for some of the types of data I mentioned. But that is NOT the same as the computer supporting a second, built-in, Hardware-accelerated display.

These displays depend on DisplayLink software, and are at the whim of Apple when they make MacOS changes. There have been cases where MacOS changes completely disabled DisplayLink software, and it took some time for them to recover.

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I think the Big Surprise for a lot of Hub/Dock buyers is that they thought they were getting a "real" display, but actually got a DisplayLink "fake" Display. If you got what you expected in every case, I would not use such pejorative terms to describe DisplayLink.

There may indeed be more to this. But you have not told us how you had it working previously.

According to all we know here, it does not, and can not work.

Your dock is not a DisplayLink device, and their Ads show that on ANY Mac, it will simply mirror, not extend, your current display.