Hi
I ran across this same issue after upgrading from v3.9.
For my install (3 sites), I had activated WP Edit through a network activate. The ‘wp_edit_buttons’ option was available in the wp_1_options table, but not in wp_2_options or wp_3_options. The fix for me was to network deactivate, then activate WP Edit individually for each of the 3 sites.
At that point, I believe you could then switch back to a network activate, but I left it as is.
Dave