I understand the meaning of the phrase "passive aggressive", but I'm having difficulty interpreting what it means in the following context:

Solution 1:

The main thrust of the speaker is missing from the quote, but s/he seems to be describing behavior that prevents someone from moving on, actually or emotionally. This resistance to moving on is there but it is not direct, the possibility of reopening the relationship or explicitly committing to an unrequited one is not considered or confronted.

Passive-aggressive being behavior characterized by "indirect resistance [..] and an avoidance of direct confrontation," (Lexico.com) this seems to fit.

Solution 2:

Firstly, let’s rewrite the phrase a little:

being held [as] hostages by our own passive-aggressive Spotify [musical] playlist

Undoubtedly, there is a metaphor in ”being held hostages”. Spotify is a streaming service, mainly focused on music. Many of us could probably have listened to sad music after some loss in the past. The same can be done, but with passive-aggressive music — or, to be precise, with songs that have passive-aggressive lyrics. For example, please take a look at a fragment from “Passive Aggressive” song by Placebo:

If you deny this

Then it's your fault

Sounds pretty passive aggressive, doesn’t it? That would be the interpretation.

Solution 3:

I believe part of the issue is that this example uses the phrase "passive-aggressive" in a manner which extends beyond the present dictionary definition

From M-W:
passive-aggressive: Being, marked by, or displaying behavior characterized by the expression of negative feelings, resentment, and aggression in an unassertive passive way (as through procrastination, stubbornness, and uncommunicativeness).

However, as a native speaker in the United States, I have often heard this phrase used to describe outwardly friendly displays, intended to cause harm or to express ill feelings. This takes the action from a passive mode to a more active one. For instance, delivering bad news with a forced and artificial smile, or couching one's words and actions so that a sentiment of derision or disdain is expressed with superficial niceties. A phrase, (again delivered with exaggerated pretense of care or concern), such as "oh please, let me pick that up for you!" when the clearly intended meaning is "I'm so tired of picking up after you, you incorrigible slob!"

Contrary to the dictionary definition, these are not passive displays, but active exaggerations of pleasantries used as expressions of dissatisfaction.

In the context of your example then, the internal mental playlist is recycling memories that in a different time would be pleasant, but under current circumstances, do no more than cause pain.

I hesitate to say this is an "incorrect" usage of the phrase, as language is an organic thing, ever evolving according to usage, but I'm tempted to call it a lazy usage. However, one could also interpret this passage to be implying that the mind just sort of "turned on the memory's greatest hits reel, and then just sort of stepped out of the room, so to speak," which would lend a passive element to the scenario.