In order to fit a character's theme, I'm looking for all the spells that are in some way related to shadows or the Shadowfell. The ones I've got so far are:

Illusory Dragon

By gathering threads of shadow material from the Shadowfell, you create a Huge
shadowy dragon...

Creation

You pull wisps of shadow material from the Shadowfell to create a nonliving object...

As well as Shadow Blade and Shadow of the Moil for their general shadowyness. Are there any others that I've missed?

Seven directly related to shadows/shadowfell

I've found seven by searching on dndbeyond.com for "shadow", "shadows", "shadowy" and "shadowfell" filtering by spells:

• 
  Shadow Blade (sorcerer, warlock, wizard) - Xanathar's, 164


• 
  Shadow of the Moil (warlock) - Xanathar's, 164


• 
  Vampiric Touch (warlock, wizard, death/grave domain clerics) - PHB, 284


• 
  Illusory Dragon (wizard) - Xanathar's, 157


• 
  Creation (sorcerer, wizard, artificer, forge domain cleric) - PHB, 229


• 
  Pass without trace (druid, ranger, trickery domain cleric, circle of the land druid) - PHB, 243


• 
  Demiplane(warlock, wizard) - PHB, 231

These spells include direct language on their association with shadows or the shadowfell.

Three indirectly related

• 
  Summon Greater Demon (warlock, wizard) - Xanathar's, 166


• 
  Forbiddance(cleric) - PHB, 243


• 
  Dispel Evil and Good(cleric, paladin) - PHB, 233-4

I didn't include these in the primary list because, while they reference the shadowfell amongst other areas, they are just as a part of the mechanic that includes the shadowfell, but doesn't really directly utilize shadows or the shadowfell.

Some Shadow-based classes provide spells that are thematic

The Way of Shadow monk grants you the ability to cast the following additional spells not already listed:

• 
  Darkness(PHB, 230)


• 
  Darkvision(PHB, 230)


• 
  Silence(PHB, 275)


• 
  Minor Illusion(PHB, 260)

The Unearthed Arcana Warlock of the Raven Queen also has an expanded thematic spell list. The Raven Queen is relevant as she is listed as:

a mysterious being who rules the Shadowfell from a palace of ice deep within that dread realm.

• 
  false life(PHB, 239)


• 
  sanctuary (PHB, 272)


• 
  silence (PHB, 275)


• 
  spiritual weapon (PHB, 278)


• 
  feign death (PHB, 240)


• 
  speak with dead (PHB, 277)


• 
  ice storm (PHB, 252)


• 
  locate creature (PHB, 256)


• 
  commune (PHB, 223)

There isn't a single class that will grant you all of these

After reviewing the classes the spells are on, there is no single class that will grant you all of these RAW.

_{Thanks to someone_evil and akixkisu for filling in some gaps.}

The following spells contain the keywords "shadow" or "shadowfell" in their description.

PHB:

Creation, p. 229.

Demi Plane, p. 231.

Dispel Evil and Good, p. 233-234.

Forbiddance, p. 243.

Pass Without Trace, p. 243.

Vampiric Touch, p. 284.

XGtE:

Illusory Dragon, p 157.

Shadow Blade, p. 164.

Shadow of Moil, p. 164.

Summon Greater Demon p. 166.

I have searched through every spell in the PHB, the XGtE, the EE and the SCag.

My keyword search was done manually, and I have searched through each of the four books by flipping through the pages and reading through the spell description of every single spell throughout the entirety of the Players Handbook, Elemental Evil, Xanathars Guide To Everything and the Sword Coast Adventurer's Guide.

Thanks to IT Alex and Someone_Evil for reminding me to specify this last paragraph of my method used which further explains how the keyword search functions that I employed.

Further notice:

You are trying to build a character that thematically uses the Shadow and the Shadowfell, so it is likely that you want insight into how the Shadowfell affects creatures and the abilities of creatures. The following resources help you with that (this paragraph got added thanks to NautArch to make it more explicit on why you want to be informed about the information provided, in case that the first line and the rest of the next paragraph with the information included is not sufficient).

To gain an insight into how the Shadowfell affects creatures and their abilities read the Shadowfell DMG p. 51-52 and Planar Categories DMG p 43, and then compare Deva MM p. 15-16, Darkmantles MM p. 46, Manes MM p. 56 (also refer to Sings of Corruption MM p. 50).
The Dragon, Shadow and Shadow Dragon Template MM 84-85 are easily compared to other variants Dragons MM p. 86-118.

Shadowfell DMG p. 51-52:
These creatures are native to the Shadowfell: Undead, Cloakers, Darkmantles, Shadow Dragons, and

other creatures that thrive in the gloom

While Deva act as messengers in the Shadowfell, Manes are naturally part of lower Planes. Whether the twisted Shadowfell has an evil alignment or not is unclear.