To be clear, you're saying it takes cranking the engine over for ~30 seconds before it finally fires, runs rough for a few seconds, then smooths out and runs fine after that.

This still sounds like a fuel supply issue to me. Not the pump, not the fuel filter but a leak in a fuel supply line from the pump to the engine.

Do you have the ability to connect a fuel pressure gauge to the fuel rail and see how long it takes for the fuel pressure to bleed down after engine shutdown? You may be able to rent one from a parts store. You need the kind with the Schroeder valve (like an air fitting).
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1998 S90 088,900 and 1995 964 154,100