If you're doing semi-implicit Euler that's pretty good, per gaffer's article, semi-implicit Euler has the advantage of being symplectic, i.e. its an integration

If you're doing semi-implicit Euler that's pretty good, per gaffer's article, semi-implicit Euler has the advantage of being symplectic, i.e. its an integration method that conserves the total energy of the system you are simulating (energy conservation! physicists love it!). the particle motion in your videos looks reasonably natural, there's no obvious signs of particles seemingly gaining energy from nothing (apart from when they are perturbed by the mouse cursor), so as the resulting motion looks natural, what you are doing is fine and there's no actual problem you need to solve. if instead of simulating independent particles you were trying to accurately simulate cloth or a deformable rigid body e.g. a metallic object crashing into something, where each node in your cloth / rigid body was a particle tethered to its neighbours, that might be a whole different can of worms and justify looking into RK4 or implicit Euler where you need to solve a big linear system of equations each timestep. but you're not doing that, so no need to overcomplicate things!