I purchased the Firepower Mod (Season of the Dawn armor mod) from the Tnagled Shore Obelisk, but it does not appear as an available option when trying to slot mods into Season of the Dawn armor.
The mod shows up as owned in my collections page in-game, and also in external programs, like DIM. This appears to be a bug.
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Are you trying to put it on gear of the correct element? I believe looking at collections that it is Solar.