There's apparently a visible alt text badge on Threads now, but you have to turn it on.
Head to your profile, tap the two lines above your profile picture, click Settings, then Accessibility, and then you'll see an option for "show alt text" with a toggle next to it. Toggle it on and an alt text label will appear on images that have alt text.
From the looks of it, the alt text badge is only visible on images that have alt text added to them AND if you click into a specific post. You won’t see any alt text badges on your feed, which is just weird.
Please note that not everyone has access to this feature yet. You should also remember that not everyone (including myself) has access to the alt text field on Threads yet, so some folks may be writing image descriptions directly in their posts instead, so an alt text badge wouldn’t show up on their images despite them taking the steps to make their content accessible.
Also, Threads has new updates out as of today, so make sure you update your app!