>> For these other modes of travel, does the STP generally work (I’m thinking of bus between towns and inter-city trams and local buses?
Yes, it is valid on buses between localities, and local transport in many cities, towns and villages.
In the legend on the top right-hand side of the PDF map showing where the Swiss Travel Pass is valid, there is a red-and-white symbol that looks like a target, with the explanation "Also valid for local public transport". So, where you see that symbol on the map, local public transport is free with the Swiss Travel Pass.
>> When my son and I were in Zurich last year, we walked all over town, but I sure would have preferred taking a city tram for some of the routes ... When in Zurich, I couldn’t find info on where to buy tickets or whether our STPes were accepted.
You can indeed get free travel on local trains, trams, funiculars, buses and boats within Zürich, but unless you are also doing longer day trips on the same day, it's not cost-effective to use the Swiss Travel Pass just within Zürich.
There are a variety of ticket options for Zürich, depending on how far afield you want to travel. The main thing is to work out how many zones you are likely to travel in or through within a day, so your ticket or pass covers the correct number of zones.
The zone that covers central Zürich (Zone 110) counts as two zones. There are zone maps at tram and bus stops.
You can also use the online timetable to check which zones your intended trips will cover.
At the top of ZVV timetable page is a map. On the right hand side of the map are zoom symbols (plus and minus signs). Immediately above the plus sign is a symbol like a stack of papers. When you have searched for and selected a connection, clicking on this symbol and ticking the box for "Fare zones" will overlay the zone map onto your trip, so you can see what zones your trip will cover. Adjust the zoom to get a suitable view.
Ticket options are described here: