This is why the ground plane was invented.
I dislike breadboards, and stripboard isn't much better. Both are good ways to hook a few parts together quickly to check that they work more or less as expected, in a very rough & ready way. Once you start looking for accuracy, quietness and precision, they very rapidly become your worst enemy. I've lost count of the number of hours I wasted during my early career trying to make prototype circuits work well using these construction methods, before I eventually realised how futile it was. Please don't make the same mistake I did.
The real problem is that there is no common reference between any two points in the layout. One part's GND pin is connected to others via a resistive, inductive path across which substantial voltages can be easily developed, and the only cure for that is to eliminate that path.
You can add all the decoupling / smoothing / filter capacitors you like, but they just won't do you nearly as much good as you'd hope, because you're only ever making a signal 'quiet' with respect to a reference point that's nearby. What you're not doing, is making them quiet with respect to components that are more than a couple of cm away. Also bear in mind that the path length from a ground pin, down into the breadboard, up a capacitor leg and then all the way back down again to a signal pin can easily be a couple of cm.
That's why I generally regard a 4 layer PCB as a minimum functional requirement for many designs, and it's highly likely that you'll need to design and fabricate one before your circuit will work as well as you want it to.