Can I connect two thunderbolt monitors to my MacBook Air 15" 2023 at the same time?

Your 15" M2 MacBook Air supports only a single external display.

MacBook Air (15-inch, M2, 2023) - Technical Specifications

Assuming that both of your monitors are Apple Thunderbolt Displays, and that both of your "Thunderbolt to USB-C" adapters are Apple Thunderbolt 3-to-2 adapters, either monitor alone, should work. But your MacBook Air will only drive one.

As these displays require Thunderbolt input, there are no "workaround" products (like DisplayLink adapters) that would let you drive two of them from your computer, even if you were willing to accept the significant drawbacks that can accompany the use of such workarounds.

Duffkb wrote:

I am moving from a MacBook Pro to an Air. Previously I was able to to connect two thunderbolt monitors to my Pro. I have only two ports on my Air and one monitor connects beautifully but the other one will not connect. It still works fine with my Pro so I know it is not the monitor. Both monitors have the Thunderbolt to USB-C adapter. The monitor that does not want to connect is a A1407. Is there a reason this monitor will not connect with my Air?

See this thread: does the new macbook air 15 support 2 ext… - Apple Community

Low-spec Apple silicon (M1, M2) supports two displays, one of which is always the internal display on the laptops.

Mid- and upper-spec Apple silicon (Pro, Max, Ultra) supports more displays.

Swapping among external monitors should work.

Use an external display with your MacBook Air - Apple Support (ZA)

It sounds as if you have two identical 27" Apple Thunderbolt Displays (model A1407). Provided that both are in working order, you should be able to use either … but only one at a time.