It's up to the DM
There is currently no official 5th-edition sourcebook detailing the mechanics of the Shadowfell. Until such a companion is released, there is no correct answer outside of "It's up to the DM".
The closest official answer comes from page 50 of the 4th-edition Manual of the Planes, where it states approximately that all light sources are reduced to 50% functionality:
Gloom: The Shadowfell mutes light sources, reducing the radius illuminated by 50 percent. For example, a torch illuminates 2 squares
instead of 5; a lantern illuminates 5 squares instead of 10. Magical
light sources are unaffected.
They may not "look" like anything: they are energy sumps.
This answer is informed by the first edition AD&D descriptions of the Positive and Negative Material planes in the PHB and DMG. I reach that far back because following editions tended to build on that, though as usual editions vary. (For some 2e and 3e perspectives, see @QuadraticWizard's answer here).
Those two planes power spells (AD&D 1e DMG, p. 40)
All magic and cleric spells are similar in that the word sounds, when
combined into whatever patterns are applicable, are charged with
energy from the Positive or Negative Material Plane. When uttered,
these sounds cause the release of this energy, which in turn triggers
a set reaction. The release of the energy contained in these words is
what causes the spell to be forgotten or the writing to disappear from
the surface upon which it is written. When spell energy is released,
it usually flows to the Prime Material from the Positive or Negative
Material Plane. To replace it, something must flow back in reverse.
The dissolution and destruction of material components provides the
energy that balances out this flow, through the principle of
similarity. Sometimes this destruction is very slow, as is the case
with druids‘ mistletoe. Those spells without apparent material
components are actually utilizing the air exhaled by the magic-user in
the utterance of the spell.
They are less a "place" than a "state of being" for practical
purposes. (AD&D 1e DMG p. 112)
Deities will not intervene on the planes which are the habitation of
other deities, i.e., the Outer Planes. They will neither venture to
involve themselves in the Positive and Negative Material Planes.
As Gertrude Stein might say, "there is no there there" to the extent that deities (who can travel most anywhere) just don't go there.
Describing what anti-matter looks like is no small task, if it can be done at all(thanks, @Molot).
The Positive Material Plane is a place of energy and light, the place
which is the source of much that is vital and active, the power supply
for good. The Negative Material Plane is the place of anti-matter and
negative force, the source of power for undead, the energy area from
which evil grows. (AD&D 1e PHB, p. 120)
As to the 5e Positive plane from the question,
... the Positive Plane is the source of radiant energy and the raw
life force that suffuses all living beings, from the puny to the
sublime.
Your initial instinct in describing the positive material plane seems to be spot on. Pure light, pure energy, may overwhelm all visual senses - so how does it look? That's very difficult to describe. My estimate is "stand next to the sun with no sunglasses on (with heat protection) and describe what you see." It is such pure light/energy that it overwhelms mere mortal senses and even deities don't go there. The negative material plane is described as being its opposite. An implication of this is that they transcend the physicality of all of the other planes.
They way I've always seen it played, when they came up, is that those two planes are a physical manifestation of the Yin and Yang1. The two planes aren't so much physical as metaphysical. In trying to describe those two planes, one might as well try to describe "What does happiness look like? What does sadness look like?"
The material that became the Planes treatments in the PHB and DMG in AD&D 1e were broached in Dragon Magazine 8, which went into such esoterica as life stealing swords having a direct linkage to the Negative Material plane. In typical Gygaxian brainstorming fashion, we read ...
If it is accepted that the reason that certain creatures can only be
hit by magical weaponry is because the creature exists in two or more
planes simultaneously, then it follows that the weapon must likewise
extend into the planes in which the creature exists. (Dragon 8, p. 4)
But nothing to describe either the Positive or Negative plane beyond sources of power/energy/magic.
Len Lakofka, in Dragon Magazine #42 (page 24-30) went to great lengths to try and create a way to "play on the inner planes" which ran into 7 pages of dense text and tables, tables, tables. It was too clunky for any of our gaming groups. How things "looked" didn't rank very highly in importance in that article.
In Dragon 73, Gygax expresses that the lack of clarity had finally gotten to him, so he put together another article on how the planes worked.
Isn't it interesting to note how the Positive Material Plane sits upon
the material multiverse as if it were a plate? Observe also how the
Negative one serves as a saucer for the same body? (Dragon 73, p. 10)
What the Pos and Neg looked like, when all other planes were given a color in that article (Ethereal purple, Concordant Opposition, Brown) was left unclear.
1If I ever find the article that first gave us that idea, I'll add a citation. Might be an old Dragon magazine. It might also be some old Planescape material that I no longer possess.
Best Answer
There are limited 5e rules for the Shadowfell.
The DMG only includes the optional "Shadowfell Despair" rule where, typically up to once per day, characters may need to make a wisdom saving throw to avoid suffering apathy, dread, or madness. The DMG includes some additional flavor for the Shadowfell but I'm not aware of any further 5e-specific rules.
In previous editions it impeded magic.
Impact on magic
Shadowfell specifically originated in 4e and wasn't strictly 1:1 with the 3.5e Plane of Shadow. It's kind of a combination of the Plane of Shadow and the Negative Energy Plane, but I believe it's mostly referenced in 4e material. In 3.5e, the Plane of Shadow had explicit rules that can be found here that, among other things, impeded fire- or light-based magic:
The Negative Energy Plane also impedes magic, but for positive energy and cure spells rather than light and fire spells.
Damage/energy types
Note that 3.5e doesn't have radiant (or necrotic) damage and 5e doesn't have positive (or negative or divine) damage/energy. Spells that deal radiant damage in 5e typically dealt divine damage, like Flame Strike, or dealt untyped damage, like Sunbeam. Spells that used positive energy in 3.5e, such as Cure Light Wounds, don't mention an energy type in their 5e counterparts.
5e also lacks "descriptors," which were like tags on spells. Daylight, for instance, is "Evocation [Light]," so it would be impacted due to having the light descriptor. Fireball naturally has the fire descriptor, and so on. Although there might be some exceptions, it's generally fairly clear if a spell counts as fire or light in 5e.