Finland was really between a rock and a hard place, as the international community was basically a lame duck after the Soviets attacked Finland in 1939 by staging a false flag in the small village of Mainila. Although some in Finland tend to forget it, Sweden provided substantial amounts of men and material which helped a lot, but it wasn't quite enough. The only other player with enough muscle was Germany, to which Finland had good historical connections traditionally, going back to the days of the Finnish Civil War.
Also, East Karelia as an area was Finland's strategic target. Finland hoped to regain what the Soviets stole and to have a buffer in place for the next Soviet attack. Many Finnish people recognize the saying "If the enemy does not come from the East, they have taken a detour", a reflection upon historical facts.
As for Leningrad, Finland didn't really care about Leningrad, but Finland had to do something to keep Germany happy. According to Kastari, Finland made strategic errors in the East Karelia war effort, however it seems that Finland's aim was actually to get as short a border with the least effort [1]. Hence the siege ring which didn't really go anywhere nor do attacks against Leningrad.
[1] Kastari: Suomen armeijan toiminta Karjalan linnoitusaluetta vastaan syyskuussa 1941. MPKK, 2019
I get that Finland was in a crappy position during WW2. Aligning with the Nazi's was a matter of realpolitik.
And I agree that their involvement in the Siege of Leningrad amounted to a blocking force, but mother of god, that blocking force contributed to an absolutely horrific existence for the civilians inside the city.
One could maybe argue that if the Finns didn't help the Nazi's the Nazi's would have been enable to lay siege to Leningrad anyways, but the Finns are definitely tainted by their involvement.
I agree that the Leningrad siege was a terrible suffering for everyone inside the city, no question about it.
I'm not sure though what Finland could have done otherwise; if they had not been where they were, Leningrad would have received shelling from all sides, and like you say, the city would have been under siege anyway - possibly with worse consequences, since the Lake Ladoga route would've likely been cut then as well.
Actively resisting the Germans in their aspirations was not feasible, as Finland needed the German military muscle to repel Soviets then and in the years to come.
So, Finland could not not be there, and if Finland had not been passive, then the only option available would have been to actively contribute to the siege and fire at an innocent civilian population. I'm not saying the decision to avoid this was because of moral or ethical concerns; the reason was probably more mundanely a lack of material. Artillery shells and bullets were best reserved for soldiers and not starving civilians in a strategically uninteresting city.
A side note about the "Nazi alignment": if that taints Finns, then it should, strangely enough, taint Russians as well; even the Soviets aligned with Nazi Germany. The secret clause of the Molotov-Ribbentrop pact divided Europe to Soviet and German spheres of influence. Then, soon after the pact was signed, Poland took the first hit in 1939 with attacks by both Nazi Germany and Soviet Russia. And weirdly enough there was even a joint Nazi-Soviet military parade in Brest-Litovsk.
I mean, I'd argue Finland should have no been there. Sure, the Nazi's would have probably taken their place, but it's better than having your country associated with such a horrendous siege.
And yes, there is plenty of Nazi "taint" to go around that was pretty quickly forgotten/forgiven after WW2. The Russians are definitely the big ones, but also the Finns, the Hungarians, the Romanians, and of course the Italians.
Also, East Karelia as an area was Finland's strategic target. Finland hoped to regain what the Soviets stole and to have a buffer in place for the next Soviet attack. Many Finnish people recognize the saying "If the enemy does not come from the East, they have taken a detour", a reflection upon historical facts.
As for Leningrad, Finland didn't really care about Leningrad, but Finland had to do something to keep Germany happy. According to Kastari, Finland made strategic errors in the East Karelia war effort, however it seems that Finland's aim was actually to get as short a border with the least effort [1]. Hence the siege ring which didn't really go anywhere nor do attacks against Leningrad.
[1] Kastari: Suomen armeijan toiminta Karjalan linnoitusaluetta vastaan syyskuussa 1941. MPKK, 2019