Yes, you do need isolation here. Lacking isolation means you no longer have an isolation barrier between your MCU and inverter input or output.
This exact situation is very common, which has led to there being many options on the market for isolated gate drivers, which combine a gate driver (or two in many cases) with an isolator.
You could use a separate non-isolated gate driver and digital isolator, but isolated gate drivers make things easier. TI, Maxim, Analog Devices, Infineon, and several others make them, and there's an entire product category for them on Digikey.
Some of these are dual drivers intended to drive both sides of a half-bridge (and may include functionality specific to that situation, like enforcing dead time), which may be useful for your case.
In light of the comment below:
I don't need gate drivers, because I use a LMG2100 power stage which contains both gate drivers and GaN transistors [...]
While it would be possible to still use an isolated gate driver to drive the LMG2100's inputs, you're right that it would be redundant.
The LMG2100 half-bridge power stage (datasheet) does not include any form of isolation, though it does have a level shifter so both of its inputs are ground-referenced. This means that all inputs of all phases, unless this is being used for a multilevel converter or other unusual topology, are referenced to the same ground. This means you can use a single multi-channel digital isolator for all inputs. An ISO7760 might be suitable to drive a three-phase bridge, for instance.
Especially if operating at high speeds, be sure to check the pulse width distortion and channel-to-channel or part-to-part matching of your isolator of choice; these specifications tell you how much the isolator will affect the timing of your switching. Unless you're switching at inadvisably high frequencies, most general-purpose digital isolators should be capable of your switching frequency (though some old optocouplers may not be).
Remember that you will need a separate power supply for both sides of the isolator; there are very few isolators that integrate an isolated power supply into the part, and those that do tend to be more expensive than just using a separate isolated power supply. In all likelihood, the input side will share a power supply with your MCU, and the output side will share a power supply with the Vcc of your LMG2100. (Note, though, that some isolators may not function at the 5 V the LMG2100 requires; if this is the case, a linear regulator from that down to 3.3 V would be simple enough. An isolator simply doesn't consume enough power for the poor efficiency of a linear regulator to be a concern here.)
