So...
I read through and simulated SL75's approach to improving the buffer circuit instead of just throwing it out.
I think this is the better solution, precisely because it's not clear how much current the reference would have to drive on its own.
Based on my measurements of the capacitors, it is now clear that there is at least 10 µF present—plus an additional amount X related to the buffer capacitors for this 2.5 V in the front end.
I wanted to measure the actual current being drawn, but to do that, I need a very fine soldering tip—or a soldering iron—so I can solder test leads to an 0805 resistor.
In the end, I ordered a soldering iron for my Weller station, but it still hasn’t arrived.
That also means I can’t implement the “SL75 solution” right now.
But maybe the soldering iron will arrive this week after all...

Owon's solution for bridging the (poorly dimensioned) op-amp circuit, as introduced in PCB Rev 1.1.1, is one option, since the REF3425 can drive up to 10 µF according to the datasheet (and maybe a bit more). In addition, Owon saves the cost of the op-amp this way...
I assume that no “fully qualified” engineers were hired for the design; this is also evident from the fact that some circuits followed the recommendations in the respective IC data sheets exactly.
Removing the buffer circuit—which not only eliminated ripple but also helped optimize costs—probably earned the employee responsible the “Employee of the Year” award.
