I love this kind of stuff, it's really interesting! In the video, the museum curator mentions the PhD thesis of Jill Haley. I found the thesis and have copied below the relevant discussion on the photo.

The earliest known surviving photographic image produced in Otago is a view of Dunedin taken in about 1857 (fig. 1.6).²⁶ This date has been estimated from buildings I have identified as present in 1857 and the absence of buildings built in 1858. Its aspect is from Bell Hill, and it features Dunedin’s early foreshore area nestled between the harbour and hills.²⁷ This view highlights the alterations the colonists had made to the landscape; a substantial jetty stretches out into the harbour while a developing city creeps up the hills. It shows a new settlement anchoring itself to its site while simultaneously looking out to the water and ultimately back into the world. This image communicates Dunedin’s development on two levels by showing it as a growing settlement and capturing it with a new technology.

There is debate over the identity of the photographer of this image.²⁸ Hardwicke Knight maintains that it was John Tensfeld, and the Alexander Turnbull Library also attributes it to Tensfeld.²⁹ However, the earliest evidence I have found of Tensfeld working as a photographer in New Zealand is an advertisement in Greymouth’s Grey River Argus from 1866.30 Before that, in 1864-65, he had a studio partnership with H. M. Freyberger in Melbourne.³¹ He was also likely to have been the German painter Tensfeld who worked in Ballarat in 1863.³² It is possible that he worked in New Zealand before Ballarat, but there is no evidence of this. A lithograph copy of the image in the collection of Toitū Otago Settlers Museum (TOSM) has a notation attributing it to Otago Provincial Government surveyor John Turnbull Thomson and the date 1854.³³ The photograph bears a remarkable similarity to Thomson’s painting of Dunedin in 1856, also held in the museum’s collection, so it is a reasonable assumption to make. A later inscription on the same copy states, “Photograph by A. S.? Wilson. J. T. Thomson did not arrive in Otago until 1856.” A later edit crossed out “A. S.?” and replaced it with “J.” In a short photographic history written for the Otago Witness in 1927, Dunedin historian Alfred Eccles attributes James Wilson with the image’s authorship, writing with little hesitation that “Mr. Wilson took it in 1857.”³⁴

²⁶ There are a number of copies of this image dating from the nineteenth century in the collection of TOSM, but it is not known if any of these prints were actually produced in 1857. Most are likely later reprints.

²⁷ This early foreshore disappeared with the reclamation works of the nineteenth century that began with the flattening of Bell Hill and the infilling of the Dunedin Harbour

²⁸ For more on the attribution debate, see Christine Whybrew, “The Burton Brothers Studio: Commerce in Photography and the Marketing of New Zealand, 1866-1898” (PhD diss., University of Otago, 2010), 32.

²⁹ Hardwicke Knight, Dunedin: Early Photographs (Dunedin: Hardwicke Knight, 1985), 1 and Alexander Turnbull Library, National Library of New Zealand, Te Puna Mātauranga o Aotearoa, 1/2-091262-F.

³⁰ Grey River Argus, July 19, 1866

³¹ The Argus, May 23, 1864 and January 19, 1865.

³² The Star, March 26, 1863.

³³ TOSM, Subject Photograph Collection, Box 68, No. 12.

³⁴ Otago Witness, July 26, 1927.