Starting at your link, on the far right in the first row is the SEC yield, which is the yield that is most commonly used to estimate future returns.
The distribution yields are based on what the fund actually distributed at the end of each month, and currently are higher for most bond funds. This is because the funds hold bonds priced above par (face value) that have higher coupon payments. As the bonds approach maturity, the values of these "premium" bonds will gradually decline. The SEC yield is a form of yield to maturity (YTM) that factors in this gradual erosion of bond value into the yield, which is why it is lower.
The SEC yield is an average YTM based on the previous 30 days. If rates rise quickly, it is likely to be somewhat lower than the average YTM for the fund. This is why I am being generous and bumping it up a bit; also, I usually use yields for Admiral shares, which are a bit higher.
You can see yields for all Vanguard bond funds by going to Vanguard - Vanguard funds
, the selecting Bonds under Asset Class on the left. You can then click in the style box to select a subset of bonds. Click the top middle box (medium maturity, high credit quality) to see TBM and other high-quality intermediate-term bond funds. I see TBM admiral shares by default, since $10,000 is selcted by default on the left. You can select $50,000 to show only admiral funds of the other funds (you also can select Admiral shares lower down).
SEC yield is shown on the default "Performance" tab. You can select the Distributions tab to also see distribution yields. The SEC yield of TBM admiral is 2.01%. You can see average YTM by selecting Attributes & Expense Ratio tab, then Bond attributes. Average YTM of 2.3% is shown as of 6/30. Rates haven't changed much since 6/30, and the fund expense is 0.1% (YTM does not subtract expenses, SEC yield does), so I guestimate the current average YTM, after expenses, as about 2.2%.
For the Pimco bond funds in your plan, your plan should provide the SEC yield somewhere in their literature or on their website. I believe this now is required. You also can go to the Pimco site and look it up, since mutual funds are required to provide SEC yield.
Also note, since Pimco bond funds are actively managed, they could do better or worse than TBM based on the bets the fund managers make.
Yes, you receive the dividends. I think in a 401k/403b plan they are automatically reinvested, and you may not see them directly on your transaction history. They may be shown on summary performance reports or monthly/quarterly statements.