Can I connect the TC to my Macbook Air with a Lan (TC) to USB MacBook) adaptor?
MacBook Air 13″, macOS 10.15
Can you? Yes
Will it work? Different answer. For example, say your MacBook Air is connecting to your Wi-Fi network (it likely is). The Time Capsule will be connected over Ethernet (Thunderbolt), so you will have to Turn Off Wi-Fi on the Mac when you connect to the Time Capsule to back up, then when the back up has completed, you will have to turn the Wi-Fi back on so the Mac will reconnect to your Wi-Fi router.
So yes, it will "work" sort of, but most users would find this way too cumbersome to use on a regular basis.
The correct setup would have your Time Capsule connecting to your Wi-Fi router using a permanent wired Ethernet cable connection. Then, you can select your normal Wi-Fi network that the Mac is using and back up over that Wi-Fi connection to the Time Capsule without having to "change connections" to back up.
In other words, you won't be using the Time Capsule Wi-Fi, so you could turn off the Wi-Fi function on the Time Capsule if you wish.