Soulmate is a relationship status that your sims will have if they have close to max friendship and romance bars at the same time and shows how they feel about each other.
Spouse is a relationship status that your sims will have after getting married. It should replace the "engaged" status they got when they got engaged.
After marriage, they should have both, like my sims do:
Spouse will not change until they stop being married, but soulmate should be dynamic depending on their relationship status (e.g. if the friend or romance bars drop enough they could stop being soulmates but still be married).
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So your married couple having soulmate relationship isn't a bug.
Sometimes it takes a loading from one zone to another for sim relationship panels to update. Does the "spouse" relationship bit appear after you travel somewhere and then return home or quit the game and then load it back up again?
As for the whim not completing when they got married, that's a long-time bug that they should have fixed but then probably broke again - it's already been reported in this bug thread: Marriage whim not being fulfilled.
