It's possible to get around on Muni without a Clipper card, you'll need to use the MuniMobile app. Don't know the history why SF have not integrated Muni and BART together but it is what it is.
With multiple ways of paying, buying your Muni bus, rail or cable car tickets is easy. Clipper®: Use your Clipper card on all Bay Area transit systems, including Muni. To pay for your trip, tag your Clipper card or Clipper mobile on the ticket readers inside Muni vehicles and at Muni Metro fare...
www.sfmta.com
I used my Wise virtual visa card (possibly via Google Pay) to purchase fares on the MuniMobile app earlier this year; all of the "MuniMobile" fares listed on the SFMTA link above were available for purchase.
You can purchase the fares in advance and you then have (IIRC) 6 months to activate the fare for travel.
I stayed with relatives in Daly City, so I purchased the Day Pass without Cable Car (it was $5 last year, went up to $5.50 earlier this year and is now $5.70) and traveled exclusively on Muni (did not use the BART).
The fares that you activate on your mobile are just images and date/time with some moving stripes (to indicate it's not a screenshot). Don't need to show the fare to bus drivers, just hop on.
Muni fares include the Muni metro system which shares some stations with the BART. To enter you have to go through fare gates but the MuniMobile app fares don't have any NFC or a QR code to scan at the gates; instead you have to go to the control booth and show the guy your MuniMobile fare and they'll open the gate for you to pass through.
I travelled 4 days on the Muni so I bought a Day Pass on the day I travelled and activated it before my first ride. On day 3 I noticed my 2nd day fare was still available for me to activate. On day 4 I noticed my 2nd day and 3rd day fares were available for me to activate. Ended up doing the right thing and purchased 4 day passes across 4 days; not sure why the mobile app thought I didn't activate the previous fare tickets. Never did get asked to show my fare, except when going through the shared Muni metro / BART stations for gate access.
MuniMobile fares only cover Muni travel, so if you intend to use both Muni and BART then it may be best to use the Clipper card instead.