Could the power adapter which I purchased from Apple Canada works for my MacBook Air M which was purchased in Mainland China?

Apple power adapters can handle all of 110/220 V and 50/60 Hz, i.e. anything worldwide, through exchangeable prongs or plug adaptors. The battery in the laptop is the same worldwide per model.

Power adapters have a maximum Watt rating. For MacBook Air M1/M2/M3, your power adapter should be rated for at least 30W/30W/35W respectively. Double that (--/67W/70W) for fast charging.

Do you mean exchangeable prongs and plug adaptors as Apple World Travel Adapter Kit - Apple (CA)?

If you use you power adapter in the same country as where you purchased it, then you wouldn’t needs additional

exchangeable prongs or plug adaptors.

My case is, I want use the original power adapter (with its cable) at home,

It wasn’t clear to me where this setup would be used. Canada or China or somewhere else?

and purchase another new 70W USB-C Power Adapter - Apple (CA) and USB-C to MagSafe 3 Cable (2m) - Silver - Apple (CA) for my office. So, if I understand you correctly, I can use the both new ones on my MacBook Air M2 (220V) directly.

MacBook Air (2022 or later) and MacBook Pro (2021 or later) can use the MagSafe 3 cable. Charging through Thunderbolt/“USB-C” is still supported as well, but probably slower. You can use multiple power adapters for different locations; no need to use the bundled one. For the MacBook Air itself, it doesn’t matter where it came from, concerning the power supply. The only concern is the power plug type and the AC wall socket compatibility. The rest is automatically ‘negotiated’. You should be fine with these purchases.

my MacBook Air M2 (220V)

The MacBook Air itself uses a much lower DC voltage: 14.5V, I believe (20V for the 15" MacBook Pro). It is the power adapter brick that converts 220V or 100V AC from your wall outlet to a lower voltage DC that the device and its battery can handle.