The mechanical part is short: get the VOD file, cut a 15 to 60 second moment out of it, crop it to 9:16, burn in captions, upload. YouTube treats any vertical or square upload under three minutes as a Short automatically, so there is no separate publish button to hunt for. The hard part is deciding which 40 seconds out of a six hour stream are worth cutting, and that is where all of the time actually goes.
Get the VOD before it expires
Twitch keeps past broadcasts for 7 days on most channels, 14 days if you are a Partner or have Turbo. That deadline is the first real constraint on this whole question. If you are not already exporting VODs somewhere, the archive you are planning to mine does not exist yet.
Downloading from the Video Producer page gives you the source file. Clipping inside Twitch gives you a 60 second maximum and another round of compression, which is fine for a talking head moment and visibly bad for fast gameplay.
What a Short needs from a 16:9 stream
Vertical means you are throwing away most of the frame. The two normal answers are cropping tight on the action, or stacking your facecam over a cropped game view. If your cam was small in a corner, that stack looks rough no matter how good the editor is, and the fix belongs on the stream side. A second vertical scene, or a bigger cam, saves you an argument with the crop every single week.
Finding the moment is the actual job
Clipping live is the cheapest option and the least complete one. You get the moments you noticed while they happened, which skews toward loud reactions and away from the good five minute explanation you gave without thinking about it.
Scrubbing the VOD yourself works and does not scale. A six hour stream at 2x is three hours of watching, per stream, forever. People do this and then quietly stop doing it around week five.
Chat is a decent free index. Download the chat log with timestamps, look at where message rate spikes, jump there. This works well on a busy channel and does nothing on a quiet one, and it only ever finds the loud moments, same as clipping live.
Auto clipping tools score a VOD on audio peaks, chat activity, and keyword hits, then hand back ranked candidates with captions and a reframe already applied. They are genuinely fast. They are also tuned for what looks clippable, so they reliably miss the quiet segment where you explained something well, and most of them want the whole multi hour file uploaded first, which is its own afternoon.
Then there is searching the archive by what is in it: index each recording once, then ask in plain language and get timestamps back. The question this answers is broader than any single VOD. "Where have I ever talked about the patch that broke my build" is a different question from "what happened on Tuesday", and it is usually the one that produces a series instead of a one off. Vivu does this against footage that stays in your existing storage, so asking across 200 hours does not start with downloading 200 hours. It gives you the timestamp and stops there; the cutting, the captions, and the vertical crop still happen in your editor.
If the VOD is already on YouTube
If you are exporting full streams to YouTube anyway, Studio can carve a Short out of an existing upload directly, no download and no local editor. It is limited compared to a real edit and it is free, and for a channel testing whether Shorts do anything for it at all, that is the correct first experiment.
When you do not need a system for this
If your Shorts come out of this week's stream, you already have everything you need. Clip live, cut one session a week, done. Any tooling on top of that is solving a problem you do not have yet. The same goes if you post one Short a week: the selection cost is small enough that a person doing it by hand is cheaper than anything else, and probably better at picking.
The line is how far back you are willing to reach. If the answer is this week, tooling is overhead. If you want the running joke you have done twelve times across two years, or the thing a viewer half remembers from last spring, you need the archive to be searchable, and there is no amount of discipline during the stream that gets you that retroactively.