Fan runs loud even when the laptop is idle, nothing heavy open

Check what the GPU is doing. On Linux I would just look at the sensors, on a Mac you can use Activity Monitor and the GPU history window. If it is the discrete GPU running all the time, that would explain the fan and the heat, and it would fit with the monitor being the trigger.

Just install a fan control app and set the fans to a fixed low speed. The Mac is way too cautious. You can run them at 1500 RPM and it will be fine, I did the same thing on my Windows laptop and it never got hot.

Sophie, two quick things before you change anything. First, quit apps one at a time and watch whether the noise drops. A browser tab or a background sync can hold the CPU in a state you do not notice in a quick glance. Second, restart. It sounds dull, but I have seen fans go quiet after a clean restart more often than I would like to admit.

@Tyler B. forcing fans low on a machine that is already thermally tight is how you end up with throttled exports and a hot palm rest. Noise is annoying, heat shortens a laptop's life.

Not a Mac user, but my work laptop does this when I use it on a pillow or a blanket. The vents get blocked and the fan runs hard just to keep it level. Maybe worth checking that the surface is not soft.

This is known behaviour on Macs with two graphics chips. Connecting an external display makes the computer use the high-performance graphics chip until you disconnect it, so a louder idle fan is expected. Check Battery settings for automatic graphics switching, and see whether the noise drops with the display unplugged. If it does, it is working as designed.

Apple's page on setting graphics performance on a MacBook Pro says the "automatic graphics switching" option is on by default, and that if you connect an external display the computer uses the high-performance graphics processor until you disconnect it. In macOS Ventura or later you reach the setting with Apple menu, System Settings, Battery, then the Options button. If you do not see the option, your Mac has only one graphics system. Because the display forces the discrete chip, the setting may not change anything while it is attached, so test with it unplugged first.

On the dust question, Dell's troubleshooting guide says that clogged air vents can cause a fan to run constantly, and that you should turn the computer off and disconnect power before using compressed air, and never use a vacuum cleaner or blower because they can cause static. It is a Dell article, but the general safety advice holds for any laptop. Keep it on a hard, flat surface so the vents can breathe.

Tyler, I would not lock the fans low. The fans exist to keep the chips from overheating, and forcing them down trades noise for heat. Leave the fan curve alone.

@Ines Calder that fits. I unplugged the display and the fans settled to near silent within a few minutes. I will try the display on a lighter workflow and see if it is acceptable, or consider a different way to connect it. Thank you.