HDMI Input Not Supported on 2021 MBP

to get a Mac display to become active, you need the Mac to query the display, and the display to answer with its name and capabilities. Otherwise, the display will not be shown as present, and no data will be sent to the display. "No signal detected" or "input Not support" is generated by the DISPLAY, not by the Mac.

 It is possible you have set your built-in display and external display to [√] Mirror displays. This will produce a 'compromise' resolution, intended for BOTH displays to use simultaneously, but occasionally one display or the other can not quite met the predicted compromise:

in this illustration, you can see that the TWO blue Icons for screen area almost completely overlap, indicating mirroring.

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Try unplugging the display cable from the laptop and reconnecting it. I was just working on a 2019 Mac where it had trouble using an older display where the display mentioned those issue. Reconnecting the display to the Mac after the Mac has booted or woken from sleep may help. If this is the case, then you likely have a compatibility issue between the display and this Mac. I have also seen reports on these forums regarding HDMI issues so you could try connecting the external display using a DVI connection instead by using an appropriate USB-C to DVI adapter.

The other thing to try is to review the "on-screen display" setting. This is done separately, in the display itself, to see if any settings might be precluding proper operation.

Displays Preferences shows SCALED resolutions. These are NOT the Hardware resolutions you display is set to. These are effective resolutions for TEXT when displayed on that display when you select Scaled.

They are intended to be a convenience for you, but they often cause concern and outright alarm instead.

To see the ACTUAL resolution your display is set to use:

 Menu > about this Mac > (system report) > Graphics & Displays

Select your display and scroll around until you see two items.

The first is self explanatory: 'Resolution:' e,g., 1920 by 1080

This is the hardware resolution at which your display is operating. Graphics are drawn at this Actual Resolution. But there is a problem -- If text were displayed at the Actual Resolution, on HiDPI displays it would be microscopic and unreadable.

The second resolution shown is 'User Interface Looks like:' this reveals the apparent size of text displayed on your display after scaling is applied ONLY to textual items.

Text is rendered at full resolution, then SCALED by the display Hardware by a factor (like 1.2 or 1.5, or 2.0) before it is aded to the display buffer. This makes it fully readable, yet maintains crisp edges that would be lost otherwise.

That is not considered a Hi DPI display, so it should not be set to Scaled.

its native 1600 by 900 at 60Hz should be supported directly over HDMI 1.4, not scaled.

Are you using adequate cables?

HDMI cables you want for HDMI-only Monitors (higher resolutions than 720p TV sets) are marked as Certified with an anti-counterfeiting tag and are labeled:

"Premium High Speed HDMI cable" or that + "with Ethernet" --OR--

"Ultra High Speed HDMI cable" or that + "48G"

Cables with No Certification tags are good for your standard 720p TV set, and not much more.