In article ,
says...
The board has a sticker indicating that it is a replacement from
1990. Jumper B30 has been cut. My literature indicates panel is
A10320 instead of B10326.

That tracks. Replacement modules usually have most of the
latest updates. And sometimes extra parts that you don't
need, depending on what it is replacing.

What is the purpose of these caps? Filtering? What would the effect
be if I use the wrong (larger value) cap?

These capacitors "tune" the sweep circuit, for want of a
better word. It's not a resonant circuit, but you do need
to control the slew rate when the output transistor turns
off (retrace).

You may have noticed that the two capacitors are connected
in parallel. The larger value capacitor is a rolled film,
and does the bulk of the "tuning", but the circuit apparently
also needs high frequency suppression, which rolled films
are not good at, so they also put in a smaller ceramic.
Most boards also have a ferrite bead on the output transistor.

You probably would not notice much difference if you put in
a 1000pF or 470pF instead of 680pF, since this capacitor is
only about a tenth of the total. Maybe a tiny change in sweep
width. But you have to assume the maker knew what they were
doing unless circumstances compel you to do otherwise.