Do spells in the same Showdown contribute to Tryndamere Overkill damage requirement?

No, spells in the same showdown do not contribute to Tryndamere's "excess damage" requirement.

According to RiftJudge FAQ #5311 and RiftJudge FAQ #10022, Tryndamere's ability specifically counts only combat damage assigned during the combat damage step of the showdown. Spell damage dealt during the showdown does not factor into the calculation for the 5+ excess damage threshold.

While spell damage can help reduce a unit's remaining health—making it easier for a unit to take "excess" damage from combat—the damage dealt by the spell itself is excluded from the total used to satisfy Tryndamere’s ability trigger.