Mitigate TPS56* ecomode ripple effect under lighter loads
The light load efficiency mode (PFM) greatly improves the efficiency in the range where it's operational, at the expense of higher ripple and variable switching frequency.

It's a hysteretic mode, so frequency depends on the load current.

There are other parts from TI and other manufacturers that are PWM only, or selectable between forced PWM and auto-PWM/PFM modes.  One of those may be more appropriate if you're not concerned about the efficiency loss.

One example is the TPS562208, though a smaller device could be used based on your load requirements.

If you want to keep the switcher as-is, (for efficiency or convenience) the LDO will certainly help, but be sure you have enough headroom above the dropout voltage to get the PSRR you need.  As you approach dropout, the PSRR will fall off rapidly.  The datasheet doesn't do a good job of specifying this, so you may need to experiment.