Does the MacBook Air trackpad have a physical click?

Yes, what you are describing sounds normal for a new MacBook Air M5. 

A - The MacBook Air uses a Force Touch trackpad, which relies on pressure sensors and haptic feedback rather than a conventional mechanical click.

Apple confirms that Force Touch trackpads do not provide a click or haptic feedback when the Mac is turned off. (Apple Support)

B - Therefore, if you can feel a very slight physical movement when you deliberately press the trackpad while the MacBook is powered off, that does not necessarily indicate a defect. 

C - A tiny amount of physical movement can be felt even though the normal clicking sensation is produced electronically through the haptic mechanism.

D - Since your trackpad is functioning normally, has no visible bending or unevenness, and the movement is extremely small and only noticeable when you deliberately apply pressure, I would not be concerned or return the MacBook based on this alone.

E - I would also avoid repeatedly pressing the trackpad harder to test how much it moves. 

F - If you want complete peace of mind, the easiest comparison would be to visit an Apple Store or authorized retailer and gently compare your trackpad with another MacBook Air.

You can also check Apple's documentation here:

MacBook Air trackpad — Apple Support

How to force click and get haptic feedback on Apple trackpads — Apple Support

Change Trackpad settings on Mac — Apple Support

G - Apple's current MacBook Air documentation specifically identifies the built-in trackpad as a Force Touch trackpad. (Apple Support)

Your M5 MacBook Air uses a Force Touch trackpad. The normal “click” is created by haptic feedback rather than a traditional mechanical click. Apple specifically says a Force Touch trackpad doesn’t click or provide haptic feedback when the Mac is turned off.

So if you’re only noticing a tiny amount of movement when pressing firmly while it’s powered off, I wouldn’t assume there’s a problem just from that. Apple doesn’t specify an acceptable amount of physical movement.

Since the Mac is only three days old, though, I’d have Apple check it if you can feel a distinct mechanical click while it’s off, if the trackpad feels loose or uneven, or if the movement bothers you. I also wouldn’t keep pressing harder just to test it.

You are welcome