The PHB (pg 198) has that section written as such:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

Mighty villains and special nonplayer characters are common exceptions; the DM might have them fall unconscious and follow the same rules as player characters.

Note the use of most and common exceptions.

Additionally, PHB 197 has the following:

The best way to save a creature with 0 hit points is to heal it. If healing is unavailable, the creature can at least be stabilized so that it isn’t killed by a failed death saving throw.

You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check.

Note the use of creature here, not you or player character.

That makes it clear that having an enemy die instantly at 0 is an option that the DM may use. It's completely legal to rule that monsters use the same rules "Dropping to 0 Hit Points" as PCs. If you want to make sure that some of your enemies are alive after the battle to interrogate them, you should:

• Make use of the "Knockout" rule, when able.
• Otherwise, ask your GM to determine which enemies are still alive; (s)he can determine that by fiat, or by rolling death saving throws for each of the enemies.
• At this point, you should know which enemies are alive but dieing, and which are at 0, but stable, and you can move on from there.

Your RAW interpretation is correct

The interaction with lesser restoration

When casting lesser restoration on a target affected by feign death, the RAW result would be the same as casting it on a target affected by the likes of blindness/deafness, contagion, sunbeam, or any other spell imposing the blinded condition: the blindness is ended.

This is odd, though, because with feign death the target is in a state of blind and immobile catalepsy verging on death because they opted into it, not because they were harmed. My guess is that the designers didn't consider that anybody would bother to cast lesser restoration on the same target (or didn't care). The RAW leads to some narrative dissonance that I suspect isn't intended, which I'll address in a later section.

The interaction with freedom of movement

When casting freedom of movement on a target affected by feign death, there's no condition being ended. Rather, freedom of movement effectively suspends one of the effects of feign death.

Here's the relevant text from freedom of movement:

For the duration, ...spells and other magical effects [can't] reduce the target's speed...

And from feign death:

For the spell’s duration... [the target's] speed drops to 0.

In this case, we need to consult the rule for overlapping spell effects to figure out how they should interact (see Combining Magical Effects from the Spellcasting section of the Basic Rules):

The effects of different spells add together while the durations of those spells overlap.

So the RAW result is that the effects add together. But what does it mean to "add together" two directly contradictory effects? Since they're mutually exclusive, one spell has to supersede the other (or they have to cancel out, thereby imposing no movement adjustments on the target, which in this case is equivalent to freedom of movement's benefit anyway). So which one should the DM choose? Well, the entire point of freedom of movement is exactly to counteract effects like this!

Once again, by RAW, the result is that the effect of feign death should be superseded. Yet again the RAW leads to some narrative dissonance that I suspect isn't intended, so let's address that now.

How to resolve the dissonance

I have no evidence that the RAW result isn't intended. However, you're asking the question because, like me, it just feels like it shouldn't work this way. As you said in your question, "this doesn't quite seem like it's the intent of the spell." So let's operate under that assumption: that there's some dissonance to work through.

At my table, feign death would supersede the other spells, because my gut tells me that when you opt into its effects you don't get to have your cake and eat it too. At your table, you're free to use the RAW if you think it promotes more interesting gameplay or narrative (magical espionage action: "huh? what's that? it's just a body"), or you're free to share my gut feeling and declare that feign death supersedes. In any case, it's always up to the DM to run the game in a way that makes sense for them and their table, so you should do that.

My suggestion is to err on the side of the ruling that seems most consistent in your game's world and for the tone of the story you're trying to create. What works better for you: that a cataleptic creature indistinguishable from dead can see and move or that it can't? Your answer to that question will solve your problem.