I know how to measure a conventional single speaker, but for this type of speaker, what should I do?
It shouldn't be all that different: we're interested in what the direct sound and reflections look like. Although Atmos height channels would take some specialized signals, REW can send discrete 7.1 signals over HDMI, so it's down to figuring out how to mount the sound bar for measurements. You can figure out what angle on-axis is for each set of drivers/channels with some geometry, all other measurement angles can be deduced from there.
Measure each driver separately? But wouldn't this overlook some of its internal DSP algorithms, leading to discrepancies with actual performance?
It depends on what any DSP is actually doing. Of all the ways DSP could be used, there are only two that I can think of right now that would add some complexity to measuring a sound bar:
1. DSP being used on an array of drivers for beam steering, but if you measure in the far-field of the array you shouldn't have any issues. I haven't kept my finger on the pulse of the sound bar market, but I haven't seen anything outside of Yamaha's "sound projector" bars that use a complex array.
2. If DSP being used to drive sets of channels to enhance spatial cues, then there's the potential that sound from the "supporting" channels would corrupt the data of the channel you want to be measuring. But you can do preliminary testing to see what drivers are actually active when a signal is sent to a specific channel, and you may be able to work around it to get a clean measurement of each channel. And even if support channels are being used, the important thing to know is what the direct sound looks like.
Analyzing the driver layout and what speakers are active for a given input should allow you to deduce how to usefully measure the device. And if you think about it, the engineers who designed it must have had a way to measure it, otherwise they would have had a very hard developing it.
It's also likely that manufacturers are using DSP for dynamic range compression or limiting output to protect small drivers. In that case, some output compression tests would be informative.
Also, it seems difficult to ensure that sine wave measurements can be performed on specific drivers in such a highly integrated device.
Not necessarily. REW can send signal to each channel for 7.1, then you can place your mic nearfield on each individual driver to verify that sound is only coming out where you want it to before proceeding with far-field measurements. If it's not coming out where you want it, you can preform some more tests and investigations to figure out how to proceed. Testing Atmos channels would require specialized test tracks, but you can see how measuring 7.1 goes before tackling that.
Finally, what kind of directivity is considered excellent?
Likely the same as any other sound reproduction source: with the qualities of the direct sound being of prime importance, but after that, more spacious tends to be more preferred than less spacious, so wider (but not necessarily even) directivity. Especially since a soundbar will be likely be spaciously challenged by nature of the channels being close together. Having reflected sound more similar to the direct sound also tends to be connected to a higher preference.
I'd anticipate that you'll see pretty wide directivity simply because of the geometry of the bar itself and driver size's involved.