Not sure exactly how "in-depth" I can get with this answer as, ultimately, its asking why Stalin thought/prioritized the way he did. And unfortunately we can't read his mind nor did he leave us some kind of extensive journals detailing his personal thoughts. So in the end all I can provide is the more or less official reasoning and what logical factors may have influenced this.

So Trotsky was, by far-and-away the biggest political rival to Stalin during effectively his entire tenure in office. It's pretty widely known that Lenin did not want Stalin to remain General Secretary and this meant that Trotsky was most likely to take the mantle of leadership in the party. Even once sidelined and forced into exile the fact still remained that Trotsky had probably the most "legitimate" claim to leadership of the Soviet Union, he merely lacked the skilled political maneuvering and friends in high places to make it a reality. But this was not a guaranteed constant. In exile Trotsky was basically defined by his near constant campaigning against Stalinism. While somewhat marginal compared to the influence of Stalin, it nonetheless represented the most notable opposition within the left to Stalin's near-monopoly in the communist sphere.

This was a large part of why Stalin wanted Trotsky dead already, to hopefully put an end to this leftist opposition to Stalinism. This motivation was likely exacerbated by Trotsky forming the Fourth International which was purposefully intended to be an alternative power-base for communists outside of the Stalin-led Comintern. While again the Comintern/Stalin still held decisively more power/influence than the 4th Intern/Trotsky, it did not mean that he was not still viewed as a threat. There's a variety of ways in which potentially the 4th Intern/Trotsky could throw a wrench into Stalin's plans or potentially even threaten his leadership of the Soviet Union. Whether or not they ever realistically could have done this is irrelevant, the fact of the matter as far as Stalin was concerned was that it was possible.

Notably in the Great Purges Stalin did not solely purge leftist/Trotskyists. He also purged rightists like Bukharin, Tomsky, and Rykov who had previously sided with him in his power struggles against Trotsky. Clearly Stalin was not above killing those he viewed as a threat, regardless of loyalties, politics, or even evidence. So why shouldn't he go out of his way to kill the person who was arguably the biggest threat to his rule. He killed plenty of notable Bolsheviks who did not publicly (or sometimes not even privately) criticize him or his rule, why shouldn't he kill a notable Bolshevik whose defining feature was criticizing him and trying to oust him from power? Not only that, but Trotsky was also, arguably, only second-to Lenin in terms of notable Bolsheviks in the Russian Revolution and Civil War. We're talking about a seriously famous and influential figure, he may be exiled and erased from the history books, but he was certainly not forgotten by most anyone in the USSR.

So the crux of your question seems to me to be "Why was Stalin obsessed with killing him if he didn't realistically pose a big threat?" To which the answer, as best I could think of it, is that to Stalin Trotsky was the biggest threat. Even if he was not at present able to render much of a threat the fact remained that he could at some point in the future, and had already gone much further in organizing an anti-Stalin movement than arguably anyone else. So if Stalin was in the process of eliminating any and all threats to his rule (which he was) then Trotsky is a natural target.

I would recommend "Stalin: A New Biography of a Dictator" by Oleg Klevniuk for info on Stalin and his reign over the Soviet Union. You could also read Trotsky's own words on the subject in "Stalin Seeks My Death" Where he explains basically what I did here: Stalin viewed the exile as a mistake and that Trotsky could still organize an opposition to his rule even from abroad and this had to be put to an end as soon as possible.