Tremorsense and Blindsight function as 'seeing', but cannot be blocked by shadows.
Truesight is not be affected, but for a different reason.
Tremorsense and Blindsight are a little more complicated. Let's deal with them first.
Do Tremorsense and Blindsight function as seeing?
Consider the Sage Advice Compendium ruling on whether Blindsight allows one to make opportunity attacks (and thanks to Medix2 for the reference)
Can a blinded creature make an opportunity attack?
An opportunity attack is triggered by “a hostile creature you can see”. If you can’t see an enemy, you can’t make an opportunity attack against it. Creatures with blindsight are an exception to this rule, because that ability lets those creatures “see” within a certain radius.
For an unofficial explanation of what lets those creatures "see" means, the question cited by the OP contains two examples of how such senses can function as seeing:
Jeremy Crawford on Twitter states that blindsight allows you to spot an invisible creature, although that creature can still attempt to Hide.
Even more explicitly, Mike Mearls says that blindsight and tremorsense count as seeing for spells and abilities that require sight to target.
So while blindsight and tremorsense are not sight per se, within the realm of abilities that require sight, they can function as sight. To the OP's question then, both blindsight and tremorsense are eligible to be disrupted by an effect which targets sight.
But can illusion spells target senses other than vision?
"School of Illusion" (PHB118)
You focus your studies on magic that dazzles the senses, befuddles the mind, and tricks even the wisest folk. Your magic is subtle, but the illusions crafted by your keen mind make the impossible seem real.
Clearly the illusion school can create effects that are not limited to the visual. Phantom Steed, for example, creates a mount that is so tactilely existent that you can ride on it! So an illusion effect could be used to 'blind' the senses of someone with blindsight or tremorsense. Illusionary 'white noise' sound, for example, could disrupt blindsight, while illusory tactile vibrations could block tremorsense.
However, look at the description of Shadow Arrow. If it simply read "You weave illusion magic into your arrow, causing it to occlude your foe’s vision", that would be sufficient for it to to be able to stop blindsight and tremorsense. Illusion magic has that capacity. But it continues, "You weave illusion magic into your arrow, causing it to occlude your foe’s vision with shadows." Under the principals that (1) there is no fluff in spell descriptions, (2) spells do what they say they do, and (3) specific beats general, we are forced to conclude that the Shadow Arrow achieves its effects specifically through shadows. Thus, it can block only the vision of creatures whose visual systems would be affected by shadows (that is, absence of light or presence of darkness). Shadow Arrow will be specifically ineffective against creatures using blindsight or tremorsense, because those senses are not blocked by shadows. Other illusory sensory effects might work against them, but not shadows.
What about Truesight?
"Truesight" (PHB 185) (emphasis mine)
A creature with truesight can, out to a specific range, see in normal and magical darkness, see invisible creatures and objects, automatically detect visual illusions and succeed on saving throws against them, and perceives [sic] the original form of a shapechanger or a creature that is transformed by magic.
Truesight says that it can see in darkness, so trying to block it with shadows will be ineffective. What's more, Truesight specifically says it allows you to automatically make your saving throw against visual illusions. Shadow Arrow allows a Wisdom save against its illusion magic for no effect. A creature with Truesight would automatically make that save and remain unaffected.
Thomas Markov's answer uses the assumption that a creature with Truesight can be blinded to suggest that Shadow Arrow could blind something with Truesight, but that is an erroneous conclusion. That question speaks to imposing the blinded condition on something and yes, a creature with Truesight can have the blinded condition if something specifically imposes that condition. Effects do what they say they do. However, Shadow Arrow does not say it imposes the blinded condition, rather it says it 'occludes your foe's vision with shadows'. It does not overcome Truesight, which specifically says that it can see in darkness.
Tremorsense and Blindsight cannot be blocked by Shadow Arrow.
Truesight is also unaffected.