With your Swiss Travel Pass you can travel from Basel to Zermatt with any train you would like to use. (You can refer to this PDF GA area 2023, Red line represent trains, yellow ones for buses, black one for funicular, cable cars, and blue ones for boats. You can use all the services if the Lines are not dotted, dotted lines means this route is not covered, you may have a discount in this case)
You will not be able to request for a SwissPass card, it is reserved for locals who purchased a GA subscription or half fare subscription, not for the passes or half fare cards intended for tourists.) From the Matterhorn funicular website, your Swiss travel pass will give you a 50% discount. (https://www.matterhornparadise.ch/en/Information/Tickets-prices/Single-and-return-tickets-all-year-, you can find it in the section for reduction)
In short, you can prebook your ticket in voucher format and print it at home or save the paper and show the PDF at the gate.