All living creatures appear to have a soul.

According to Dungeon Master's Guide p.24, "Bringing Back the Dead":

When a creature dies, its soul departs its body, leaves the Material Plane, travels through the Astral Plane, and goes to abide on the plane where the creature's deity resides. If the creature didn't worship a deity, its soul departs to the plane corresponding to its alignment.

This strongly suggests that all living creatures, at least, have a soul.

It's more ambiguous for non-living creatures, at least in 5e lore. Undead are the only creature type who cannot be raised with raise dead, a spell which restores the soul to its body. However, as mentioned in Does an intelligent undead have a soul in 5e D&D?, it varies by type of undead whether they have souls.

The only other creature I could find with a fifth edition stat block and a clear link to the Far Realm in 5E material is the Chaos Quadropod from Acquisitions Inc. It is explicitly described as “a creature from the Far Realm”.

In fourth edition lore, any creature with the “aberrant” origin (which is distinct from creature type) is said to be “native to or strongly corrupted by the distant alien plane known as the Far Realm” (4E Monster Manual, pg 280; Monster Manual 2 and 3 instead say “native to or shaped by the Far Realm”). This includes the monsters below from the three 4E Monster Manuals, which are not in your list above and have official 5E stat blocks:

• Balhannoth
• Carrion Crawler - the 4E Monster Vault gives a more direct link, saying Crawlers came to the material plane through a portal to the Far Realm
• Chuul - also described in 5E as “survivors of the ancient Aboleth empire”
• Cloaker
• Grell
• Grick
• Intellect Devourer
• Kraken
• Mimic
• Neogi
• Nothic

Most of these are “monstrosities” in 5E, rather than aberrations.

The Foulspawn (4E MM, MM3) and the Fell Taint (4E MM2) lack official 5E stat blocks, but have clear Lovecraftian origins - especially the latter. They may be worth tracking down as third-party or homebrew conversions.