Routing the live display through reasoning_details bypassed
separate_glued_reasoning_blocks, so a reasoning-summary model's
head-to-tail bold headings glued into '**One****Two**' in the live box
while the persisted reasoning_content stayed repaired. De-glue the
detail-derived text against its own display accumulator (not
reasoning_parts — mirrored fields would insert a spurious break on the
first chunk), so display and history agree.