Assuming you are travelling within the 110 zone of the city to get to the HB, unless the ticket makes mention of this, it's likely you will have to buy a tram ticket. Difficult to say without seeing the actual ticket. Did you buy it via the app?
You definitely should get a tram ticket - I've made this mistake with my mum when arriving from the main station.... we narrowly avoided a fine.... the inspector kicked us off the tram and stood over us as we purchased the most expensive local ticket....
If it says Zurich HB - Basel SBB, then tram is not included.
If it lists your closest tram stop, instead Zurich HB, then the direct tram or bus connection to HB is included..
If it says Zurich HB - Basel SBB mit City Ticket ZVV Zone 110, then it is also. Even more you have get a one day pass for Zone 110. However, such a ticket will cost more than a single tram ride to HB plus the regular Zurich HB - Basel SBB ticket.
Easyride is using fairtiq’s software under license so it should be the same, but easyride will not combine two tickets when a through price is available.
If you get a daily ticket, for example from your commune, you get transport over (almost) the entire Swiss transport network. Including buses, trams, boats, trains, some mountain lifts, etc.
When purchasing through the SBB website or app, make you enter your local stop as the starting point (not the main station) and then you are covered, plus (generally) the price doesn't change.