The manufacturer gives you a range.
MCA of 29.9 means a 30A breaker is fine. So you could leave the wire alone, swap the breaker to 30A, done with the wire you have. This is the manufacturer telling you EXACTLY how much capacity is required to run the thing under worst case conditions, so exceeding it is neither required, nor particularly beneficial. Most of the time it will use less than that.
Max Fuse (or "Overcurrent protection") of 40A means you can use a 35 or 40A breaker if you want to, and that's also fine. If you do, you need suitable wire size for 35 or 40A, which you don't have now. If you were swapping out an old unit with 40A breaker and wiring in place, great, no need to change anything. If you choose to stay with the 40A breaker you don't need, you need to change the wiring to suit it.
Mitsubishi mini-splits are inverter drive, so they don't have huge start-up surges - they start slow and ramp up to the required speed. Knee-jerking to an oversized breaker to run them is outdated thinking.
I'm fairly certain that being specified as Minimum Circuit Ampacity (rather than just "Amps") the manufacturer has already performed the derate calculation; derating twice is not required.
Example case: I run a pair of them with an MCA of 10.9A (on 15A breakers, 240V) They are the major load on my power in winter. Actual typical hourly power use overnight, when it's basially them and the fridge, and the motion lights if a deer walks past, for the whole building recently was around 2.4KWh/h in cold weather and closer to 0.6 KWH/h in the late January/early February thaw we've just had. So 10A for the pair of them (and the fridge, but it's like 1 KWh/day) in colder wather, 2.5A for the pair of them in the thaw. Nowhere close to 21.8A for the pair.
If I go back to last year when the power company claims it was -20°F and my recollection is it was more like -16F the worst hour of the day (just before dawn) was 3.8KWh, or 15.83A for the pair and the fridge. Almost but not quite 8A actual, each.