Greetings from RojoLand!
Chances are it uses the "stereo" right-channel head for reverse-direction mono playback. You're correct—single-direction stereo player, two-direction mono player, single-direction mono recorder.
You *can* find two-track stereo commercial pre-recorded tapes, but they are collectible and spendy (plus you'd have to dig 1950s pop, jazz or classical music; if there are any early rock-'n'-roll two-track tapes out there [Elvis comes to mind], they've likely been snatched up long ago by collectors). Your machine can't deal with the much more common quarter-track ("4-track") pre-recorded tapes. There are two-track tapes being produced now, but running usually at 15 IPS and mounted on (sometimes multiple) 10-1/2" reels that your rig can't support. With the old two-track stereo tapes, there were two kinds — "stacked" or "in-line" meaning the two tracks were in dead sync with each other (as you might expect), and the older "staggered" type designed to play on machines with individual heads set apart (or staggered) which have a 1-1/4" distance between the same point in time on the left and right channels. Your deck uses the stacked or in-line type. A two-track stereo tape has no "side B" since the two tracks take up (essentially) the entire tape width.
Decks like this were actually fairly versatile for their time, but are actually transitional in nature. True stereo recorders for the home were a year or two away (or extremely expensive, being professional-level machines).
Perhaps down the road, you might acquire something like a ReVox B77 Mk-II two-track deck (I have one of these) which can make stereo tapes that would play fine on your Silvertone.
Take care,
—
J. E. Knox "The Victor Freak"