According to the Guilty Gear wiki, The thunderseal is capable of suspending the flow of time within a given area or individual. Is this power similar to how Axl Low's abilities work?
In terms of function, perhaps, but not in terms of cost.
Most OutRage Jinki require a base amount of Mana (Houriki) to be used and even controlled.
In terms of what the Thundersealed Sword did, even Ky himself is not aware the reason it activated in response to his need in saving Dizzy. If anyone would know the real powers that the Jinki have, it would be Sol, who built them.
Compare/contrast with the Ouroboros Loop "theory" that Sol spoke of, which undid the seal on Ky when he was sealed away by Valentine when she first attacked Illyria.
It's unclear exactly why she spared Ky, only that the end result caused him to be sealed away in a similar seal to that of Dizzy, though in her case, even if the seal was undone, it could not stop the sublimation that was affecting and eating away at her body.
To undo the sublimation would require Valentine to be defeated, or so it was suggested at the time, since the spells were tied directly with Valentine's powers.
Most dimensional-based theories (spells) and even barrier seals (like the one that sealed up Justice at the end of the Crusades) usually follow certain rules to be activated and triggered.
A very powerful seal would require a slow activation, or at the very least a great deal of mana to be used to make up for the amount of time it would usually take for the spell to activate.
Since Valentines are already blessed with a great deal of mana capacity, casting such spells in quick succession would be an easy feat for them compared to humans (this was also true of Justice, whom Valentines are based off of).
In Ky Kiske's particular case... because he did not have the base mana to establish the Time Seal spell to halt Dizzy's "time".... the Thunderseal itself was used up as part of the cost.
Again, why this happened, and what exactly triggered it, aren't fully known yet.
Moving on... in regards to how Axl Low's powers influence time... they have an even greater cost, greater risk, and there's less capability for them to be controlled.
The "cost" in Axl Low's case, relates to how this world's Timeline is asserted.
Throughout much of Axl Low's misadventures, any time he time slipped, it was somehow connected with his memories and emotional state. He wasn't aware of it at first, but now he has some idea of how to control these powers at will.
Axl himself would never time slip in places where he could not exist or had not existed previously in terms of logical placement. Even if he visited a place completely abandoned by humans or any other living creature... said place was still connected with past memories of places he had been before, or would later visit, or connected with people he once knew.
But as it happens, each time Axl Time Slipped... the Timeline he left previously would cease to exist, asserting a new timeline each time. That itself was the cost... and it was a hefty cost at that.
While Axl can slow down and halt time temporarily, there's an exchange involved whenever he does this. For example, if someone died in the previous timeline, so long as he asserted this current timeline, there would be no means to bring them back or alter their fate.
It's also not possible for Axl to visit previous timelines he has left behind, so even if he can "slow time", he cannot change or halt it forever, at least without consequences.
By slowing down time in "this timeline", he asserts his influence and power within this timeline itself, but because of the heftiness of his powers, he currently has no control over "how much" he can use or how much he can influence.
While Dimensional Seals (or Dimensional Prisons) can halt/isolate an individual's "space/influence", they cannot entirely halt a person's "time". A good example of this is when Zato=ONE was having a conversation with Eddie while he was imprisoned by the Conclave after his revival. Even Justice was able to temporarily influence Testament while she was inside her Dimensional seal.
Even in the case of Miyabi, the Japanese Dimensional Colony, while the barrier itself does affect space around it, and even has artificial weather and seasons within the barrier... all the Japanese residents inside aren't fully sealed, and continue their personal lives as they normally would, albeit in a quarantined state.
While the Thunderseal did, in fact, temporarily slow the progression of Dizzy's time, it still came at the cost of the sword itself.
It's still a mystery in fact that the Thunderseal was able to regenerate itself after the fact, since the cost of activating such a spell was very high.
We also do not know if the spell was later undone by itself, or if Dizzy simply broke the spell herself (VastEdge's story was vague in telling us the result). The latter of which would normally not be possible without outside influence (even if Dr. Paradigm was or was not involved).
In general, most Isolated Spaces or Barriers (like the Cube for another example), are a kind of space magic that isn't normally established without some high cost to begin with.
In Testament's case, he not only needed the blood of several victims, but his very own blood to undo the seal placed on Justice, so even he paid a very high price as well.
It is also said that the blood of Japanese people was required to activate the Zessen OutRage fans, which were the source of the Japanese Dimensional Colony Barriers for many many years.
