Which Pass for a short trip with a teen? Bernese Oberland? Swiss Travel Pass? Half Price Card?

The Swiss Travel Pass is probably the worst choice here, given that the Berner Oberland is your only destination.
Buying tickets is very easy if you use the SBB app, so that's a minor inconvenience in my book, and I would be inclined towards getting the Half Fare Card if it's cheaper!

For 4 days in the Berner Oberland. get the BO Regional Pass. If you have significant trains/places to stay before and after your Lauterbrunnen stay, a HFC may prove an economical choice as well. With an HFC, there is an additional discount on the BO Reg Pass.

Thank you both. I did some more research, and it looks like the BO pass (in combination with the Half Price Pass so we can get the Family Pass) makes the most sense for us. Either that, or just the Half Price Pass (with Family Pass) and buying tickets as we go, which would be somewhat cheaper but adds a hassle factor. I'm still working on a spreadsheet to determine the real price differential before making a final decision. Thank you for the suggestions!

You did not mention in your post where you were coming from and how, nor where you are going afterward and how. That is important information to make a decision. Lauterbrunnen sits in the middle of the country.

Good point. We'll be using a Eurail pass day to travel from Cologne to Interlaken. We haven't decided on our destination immediately after Switzerland, so will either use another Eurail pass day or just pay to get to the German border (and then use the 9 Euro pass) if we're going to be staying in southern Germany.

How many nights are you booking in Lauterbrunnen area if you intend 4 days? Are you arriving and spending 3 nights with 2 full days there, plus your arrival and departure days? Or 4 nights with 3 full days plus your departure day, or 5 nights with 4 full days there?

There is a slightly less expensive option than the Berner Oberland Pass, the Jungfrau Pass.
https://www.jungfrau.ch/en-gb/jungfrau-travel-pass/
It is not as extensive as the B-O Pass, as it only does rail as far as Brienz and does not include the Schilthornbahn at all, but you can get to Muerren with the gondola and train from Gruetschalp. You get half fare from Eigergletcher to Jungfraujoch, Since you are arrive and depart by Eurail Pass at Interlaken, you do not really need the more extensive routes to Bern, Brig, and Luzern provided by the B-O Pass. And the B-O Pass is only available in 3,4,6,8,10 day increments. The Jungfrau Pass is available in anywhere from 3 to 8 days, so might fit better for the actual number of days you are there

I will check out the Jungfrau pass, thank you. (We have 4 nights, so 3 full days to explore plus arrival and departure days.)

Once it was clear that the Swiss Travel Pass didn't make sense for us, I went ahead and bought the half-price pass (plus Swiss Family Card). Still working out the numbers for whether we're better off with an additional pass (OB (or possibly Jungfrau) bought at a discount with the half-price pass) or should just stick with the half price pass itself and buy tickets as we go.

Thanks again for the suggestion!