That monitor's MagSafe 1 plug is not compatible with MagSafe 2 and MagSafe 3 ports.
Apple sells a MagSafe 1 to MagSafe 2 converter. I don't see any converters to go from MagSafe 1 or MagSafe 2 to MagSafe 3.
MagSafe to MagSafe 2 Converter - Apple
There's an existing Community Discussions thread where Mr. Bennett-Alder surmises that MagSafe 3 uses a more sophisticated form of power negotiation and that no converters to MagSafe 3 are likely forthcoming.
MagSafe 2 to MagSafe 3 converter - Apple Community
Mr. Rayfield suggested that it might be possible to convert to USB-C ( Power Delivery ) with third-party products. One link is now broken. The other, for an "ELECJET AnyWatt MS: MagSafe 1 or 2 to USB C PD Power adapter", is still working, but brings up a page saying the $21.99 USD adapter is Out of Stock.
https://elecjet.com/products/anywatt-magsafe
I don't see much point in trying to find one of those adapters. If you want a two-cable solution for connecting the Thunderbolt Display and power to a M2 MacBook Air, the optimal one would probably be
- Running a (TB3-to-TB2 adapter + TB 1/2 cable) between the M2 MacBook Air and 27" Thunderbolt Display
- Using the USB-C Power Adapter and USB-C to MagSafe 3 cable that come with the MacBook Air
That way you would leave one of your valuable multi-purpose USB-C / Thunderbolt ports available for plugging in other peripherals.