A Samsung T7 or Crucial X9 is all you need.
Yes. For Time Machine on a MacBook Air with USB-C, any reputable USB 3.2 Gen 2 or Thunderbolt 3 SSD will work fine. You don’t need to overthink this.
The Samsung T7 has been the default for years for a reason: it’s fast enough (1050MB/s read/write), tiny, silent, and doesn’t get hot. The Crucial X9 is a cheaper alternative that’s almost as good and also uses the same USB-C connection.
One thing to watch for: encryption. If you want hardware encryption (optional), Samsung T7 has it built-in. If you don’t care, the Crucial X9 is a little slower but half the price per gig.
I wouldn’t pay extra for “Thunderbolt 3” SSDs unless you actually move huge files daily — for Time Machine, USB 3.2 Gen 2 is already faster than the backup can write.
Just get at least 1TB (512GB fills up fast with everyday backups). Don’t buy an HDD — spinning drives are painfully slow for Time Machine and fail more often. An SSD is the right tool here.
Future you will thank yourself when a restore takes 20 minutes instead of two hours.