Although not really tree-like, I have yellow rocoto plants in Dutch buckets with individual branches that are at least 12ft long. They are growing up about 6ft, drape over trellis rope, and grow back down to the ground.
F@#% that plant.If only there were more than 120 days of outside growing here. Literature says 15m in it's native region. Got to 25-30' up a sugar maple before microburst season hit.
To address the OP.... there are C.baccatums that have a very tall habit if you can support them. But if we are talking pure genetics then you have to look at Capsicum species with monopodial growth habits ie.,C.caatingae,C.rhomboideum(Venezuelan accession),C.parvifolium(not the fake one Jukka ripped everyone off with). These plants do not bifurcate and continue to grow one main stem. With all parameters the same in perfect conditions,there are no other species that can come close.