TLDR: For regional travel, use the regional card/app Clipper. Muni has no 130; that's a Golden Gate bus that nominally does not go to San Francisco. Asterisk.
You used the city agency's app (not Clipper) to buy the city pass. That is fine, but it limits you to their vehicles only. If you wanted to unlock travel beyond the City, the Bay Area has a regional platform/card/app called Clipper. Had you bought that identical pass on Clipper, you would then have a Clipper account and have been able to tap onto any regional transit except Amtrak. (of course you would have to pay a fare, and have that pre-deposited into the Clipper system, which is notoriously slow to propagate due to its architecture pre-dating affordable cellular data, secure P2PE, and the like. They're working on it.)
Muni buses are silver and red**. However, the downtown area is like an international airport. There are many private and foreign (from outside San Francisco) bus lines provide express service from their county or other faraway place.
- Golden Gate Transit across the bridge to Marin
- Samtrans down the peninsula to San Mateo county
- AC transit across the Bay Bridge to the east bay
- Westcat to Vallejo and beyonnnnnd!
They are not there to provide intra-City transit. Some must traverse the city to leave it; they make intermediate "boarding only" stops for people going to their county. They tolerate and cooperate (or do not) with a sort of "hidden city ticketing" where you hop off still within the City. (though you may need to "tap off" or be charged for the farthest zone). Tourists have been known to (ab)use Golden Gate Transit for a very fast "hyperspace jump" to Fort Point (city-side foot of the bridge). Golden Gate Transit has flipped back and forth on dis/allowing this. At last report I understand they allow it because of COVID, but their local fare within San Francisco is downright punitive.
Decades ago, GG once permitted this on a Fast Pass but never on a tourist passport (not sure why; that's the perfect use). Such agreements broke apart decades ago because of the ongoing morphing of regional transit.
I hear from some a hidden gripe that the Bay Area doesn't have a single regional transit system. Feel free to line up at City Hall to sound that complaint; to get to the back of the line, take CalTrain to Morgan Hill :) But in fairness Clipper ain't terrible; it's only a problem if you want to take Amtrak or go to Rio Vista (which is closer to Sacramento than San Francisco anyway).
** Well, the surface streetcars (trams) aren't silver and red, are bedecked with historic liveries of dozens of cities which used PCC type cars. But none of those cities are close enough to be a confusion, and being rail, it's obvious they are limited by their infrastructure. And Muni passes are not valid on cable cars, except for certain specific and costly tourist passes.