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It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spirits are kind of creature. Event the explaination of monster/player sizes is under the heading "Creature Sizes". All monsters, NPCs or PCs are creatures (including fey which a fey spirit would be).

We see that in the next line, it starts refering to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and less useful spell. Find Familiar uses the same language "You gain the service of a familiar, a spirit that takes an animal form..." If they weren't creatures they couldn't be targeted by any spell that says "Target one creature within range..." or "All creatures in the area must make a ... saving throw..." Meaning they'd be invincible.

It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spirits are kind of creature. Even the explanation of monster/player sizes is under the heading "Creature Sizes". All monsters, NPCs or PCs are creatures (including fey which a fey spirit would be).

By Counter Example

We see that in the next line, it starts referring to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and much less useful spell. Find Familiar uses the same language "You gain the service of a familiar, a spirit that takes an animal form..." If they weren't creatures they couldn't be targeted by any spell that says "Target one creature within range..." or "All creatures in the area must make a ... saving throw..." Meaning they'd be invincible.

It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spirits are kind of creature. Event the explaination of sives is under the heading "Creature Sizes". The only monster, NPCs or PCs that are not always treated as creatures are constructs (and possibly Gods, but 5e doesn't print stat blocks for them anyway).

We see that in the next line, it starts refering to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and less useful spell. Find Familiar uses the same language "You gain the service of a familiar, a spirit that takes an animal form..." If they weren't creatures they couldn't be targeted by any spell that says "Target one creature within range..." or "All creatures in the area must make a ... saving throw..." Meaning they'd be invincible.

It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spirits are kind of creature. Event the explaination of monster/player sizes is under the heading "Creature Sizes". All monsters, NPCs or PCs are creatures (including fey which a fey spirit would be).

We see that in the next line, it starts refering to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and less useful spell. Find Familiar uses the same language "You gain the service of a familiar, a spirit that takes an animal form..." If they weren't creatures they couldn't be targeted by any spell that says "Target one creature within range..." or "All creatures in the area must make a ... saving throw..." Meaning they'd be invincible.

It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spritis are kind of creature. The only monster, NPCs or PCs that are not always treated as creatures are constructs (and possibly Gods, but 5e doesn't print stat blocks for them anyway).

We see that in the next line, it starts refering to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and less useful spell.

It should not get Legendary Actions

So, we have the line from the spell conjure fey:

You summon a fey creature of challenge rating 6 or lower, or a fey spirit that takes the form of a beast of challenge rating 6 or lower. It appears in an unoccupied space that you can see within range.

The part tripping you up is bolded. You are assuming that spirits are different from creatures but that isn't the case. Spirits are kind of creature. Event the explaination of sives is under the heading "Creature Sizes". The only monster, NPCs or PCs that are not always treated as creatures are constructs (and possibly Gods, but 5e doesn't print stat blocks for them anyway).

We see that in the next line, it starts refering to both options as "the fey creature":

The fey creature is friendly to you and your companions for the duration.

If the fey spirit were not a creature, it wouldn't have to be friendly to you which would make the spell a much more interesting and less useful spell. Find Familiar uses the same language "You gain the service of a familiar, a spirit that takes an animal form..." If they weren't creatures they couldn't be targeted by any spell that says "Target one creature within range..." or "All creatures in the area must make a ... saving throw..." Meaning they'd be invincible.