Ok. First off, we should keep in mind that even in the real world 1910s, the mindset concerning these things were very different from ours, and this mindset is even more departed in the setting. Also that my commitment to the rule of cool is greater to that of realism, as expected from the genres I'm coming from.
In the setting, as it were in the real world, a lot of places expect nobles to be carrying swords with them, and be proficient in their use. It isn't relevant that guns made melee obsolete, swords still carry an important symbolical meaning and people wouldn't question their use. That was the case even in our time-line.
As for technology, it's similar to what we had in the same time period, but with the addition of magic making somethings (like petals) and machinery more feasible (it mostly boils down to having this special power source).
As for petals, they would be both capable of melee combat and ranged one, with different models being optimal for both or specialized in one (once I share some more model examples, that will be more clear)
Petals are controlled analogically by the pilot like a power armor so, if the user is a proficient swordsman, their melee capability with them would be great. They basically increment the users power.
As for unmounted combat, it's viable with heavy armament (how the military would do it), but also with a highly trained squad of knights supported by a mystic and holy magic, that was how it's done in ancient times; this role is replaced by petals currently. Basically, a trained pilot with her soul well synchronized with the petal would have a greater fighting capability than a whole army unit, but they still can fend off the monsters with some effort. Finally, a clever pilot could fend off a threat with good thinking, and melee against a monster would be very risky, but doable.
I must say we're probably thinking too deep about this, realism isn't the focus here: okay, shamons are really dangerous and tough, but a great hero from ancient times was able to defeat an invasion in an epic battle; stuff like that.
As for mystics, that's a point I still must elaborate a bit upon. It should mostly be equivalent to the magic used by your typical DnD cleric/paladin, so stuff like barriers, seals, shamon fending auras, weapons and armor blessing, etc. They play a big part in the building of petals. Accomplished mystics dedicate their whole life to the art and need decades of study to reach that point, but people can use lesser forms of it with some study and dedication. The power of a mystic is also linked to the purity of their heart, power of their soul and so forth. So, on exemplary (but non limiting) ideas of PCs who have some magic power, it could be: someone with a single inate power, maybe inherited from her lineage, someone more scholarly inclined and someone with a clerical role (like a miku priestess) and so forth.
I'm still working on magic, I don't want it to be like fireball stuff, but still be open enough for a lot of ideas and uses.