Solutions vary widely with application, so there's very little concrete that we can suggest, given that you've said nothing about [your application].
That said, I will take this as license to propose a solution for any application within this space, and leave it up to you whether such an answer is wrong for your case (since, after all, only you can know).
Consider two options from this project:
In this power-input section, AC mains is rectified and filtered (PFC stage omitted), and low-side current sense is used to measure power into the inverter (DC_P is measured elsewhere). The NB components are net bridges, zero-ohm resistors implemented in the PCB itself, placed under R4 to create Kelvin connections. This measured input rather than output current, and the purpose here was measuring the average, DC, to calculate real power, but the ripple in this measurement is still given by the inverter (output) current, give or take the effect of supply bypass.
In the INV section, we have a half-bridge inverter with bootstrap gate drive, and a current transformer sensing output. A Pulse Electronics PB0026NLT was chosen for adequate current ratings, ratio, and bandwidth.
Since the inverter is half-bridge, and the supply is single, load current must return through a coupling capacitor, or capacitor divider; some of that load current therefore will be missed by the low-side shunt. If it were full-bridge, supply (and ground-return) current will be representative, as instantaneous load current always flows from the supply, given or take inversion due to inverter state (hence "inverter"..!).
Current transformers, are not created equally. The upper and lower cutoff frequencies must be taken seriously, as well as the ratio, flux rating, burden resistance, and so on.
A negative example (or, how not to sample current): the Triad CST206-2A has an extremely strong split resonance just above the 200kHz limit. (IIRC, it's two closely-spaced peaks, say 260 and 270kHz. The ringdown waveform has a bouncing amplitude envelope to it.) Due to how it's constructed, the winding has fairly high self-capacitance, but especially the slow-wave structure of the toroid winding and high-mu core gives a low resonant frequency with a fairly high characteristic impedance. As you'll typically be using low-value burden resistors (say 100Ω) with it, the resonance is hardly damped, and its overshoot and ringing dominates the step response.
The equivalent circuit is a series-resonant trap in parallel with the burden resistor, excited by incident current; thus it keeps on ringing unless your burden resistor is as large as Zo. But that's impractically large (~kΩ), both in terms of signal level (so, you could use a resistor divider, that would be fine) and flux (which would raise the LF cutoff). You can't effectively filter out the ringing, because you need a tuned circuit to match it; without adding precision inductors and trimming, you can only cut well below it to ignore it, but then you miss much more of the waveform of interest. Thus the well-behaved practical system bandwidth might be 50kHz or less(!). And now that 20kHz minimum starts looking rather close by. (At least with a low-value burden resistor, flux won't be as much of a problem, and likely performance will extend down to a few kHz, give or take exact amplitude and phase requirements of course.)
Low-ratio toroids, and bobbin-wound (often SMT) types, generally offer good bandwidth. The PB0026NLT is rated to 500kHz, and in the circuit tested, it was I believe well-behaved to a few MHz -- not as in you're getting accurate measurements up there, but that the harmonics of a say 50kHz switching waveform are falling off (and in an orderly manner!) up there, making it suitable for, for example, peak current mode control schemes.
Current transformers, of somewhat specialized design/optimization, are quite suitable for revenue grade metrology. That is, they are accurate enough to be used for metering and billing of electrical customers. These will be low-frequency types made for mains frequency application of course, but similar principles could be employed at inverter frequencies if such accuracy were required. Components may be special order.
Others
There are also Hall effect sensors, which tend to be much less sensitive -- less accurate, more noisy -- but are sufficient for most control purposes (say, >40dB SNR), and I've used them in custom buck and inverter circuits many times.
There are also many hybrid types of sensors, for example a Hall effect sensor might be mixed with a current transformer to extend bandwidth beyond the GBW limit of the Hall sensor and its amplifier; or a compensating winding might be used, with a nulling sensor (whose gain and linearity therefore aren't too important), extending frequency response. I believe LEM has some products of this type.
There's also a saturating ribbon or fluxgate method, where a controller dithers the compensating winding to alternately saturate a small magnetic element. This transforms the system into an AC chopper amplifier of sorts, extending bandwidth all the way to DC. Vacuumschmelze for example has some products of this type.
Networks
Particularly for higher bandwidth (MHz+), current transformers give way to more general hybrid networks and coupled transmission line structures; which it seems you're at least aware of, but maybe don't know how best to apply in a switching inverter context.
For RF networks to apply, the inverter output must flow through a port. This is a single pointlike connection, upon which the instantaneous voltage and current can be measured, and through which waves (of some given system impedance) propagate to the left and right. Thus, we have incident and reflected power across a boundary, and can use various networks to measure it: voltage, current or power tap; directional bridge; etc.
For such networks to apply, to be useful, typically the load will be a matched resistance, so that reflection is small, and thus VSWR. Frequency may also be narrow, though wideband examples exist. (Making very well balanced, ultrawideband directional bridges is nontrivial; this is part of the expense of a vector network analyzer (VNA).)
This however, is at odds to the standard practice, and main advantage of, switching circuits: we specifically depend upon the reflection of excess incident power, from a reactive (namely, inductive) load, so that switching can be fast, while dissipating little power at corresponding harmonics (specifically, harmonic energy is reflected back in-phase, and "stirred" back into the DC supply -- hence why a bypass capacitor is required). We might still employ such techniques after some filtering, so we aren't measuring meaningless harmonics, and we might have modest bandwidth and well-defined characteristic impedance towards the output. But, such techniques are perhaps not quite as useful for raw switching outputs.
