SEC yield is a rough estimate of how much you'd earn in a year. And it can vary quite a bit compared to the actual yield, aka distribution yield. Neither is a guarantee of course.
Yes, you can compare SEC yield of one fund to another. That one of the main reasons for the SEC yield.
One way to see how a bond fund accrues and pays out dividends is to look in the prospectus. For the Short-Term Federal fund, it's at https://personal.vanguard.com/pub/Pdf/p ... 2210158406.
Search for "Fund Distributions", and you'll see "Income dividends generally are declared daily and distributed monthly".
So you accrue the dividends every day you hold the fund. Meaning the NAV of the fund won't drop on the distribution date, at least not because of the distribution -- it might drop because bonds in general dropped.
Another way: after you login to vanguard.com, click on "My Accounts" and then "Balance & Holdings". Then click on the "Balances by date" tab. Look at the table -- one of the columns is "Accrued dividends". You'll see an amount for your VSGDX holding.
For more info, see this wiki article or this other post.