The UNSC returning to outdated and even straight-up obsolete weapon designs makes sense in the aftermath of Halo 5: Guardians' campaign, as the A.I. rebellion and subsequent Created conflict meant most modern and link-networked equipment were compromised. So newer builds of older weapons were commissioned, and in some cases like the VK78 Commando are outright reproduced to serve a new post-A.I. conflict. It would also explain why rejected equipment like the Grappleshot would be forced into usage.
The UNSC being so thoroughly beaten by the Banished in a big off-screen war is likely due to the sudden lack of AI support. Beyond just being in a losing war against Cortana and the Created, the UNSC relied on AI to the point that they were crippled against both forces.
Furthermore, it might seem odd that Echo-216 claims his Pelican is unarmed when it very obviously is equipped with at least a front-mounted machine-gun... Until you learn that He stole the very first dropship he could find on the Infinity with the intention of getting the hell out of there — hence he wouldn't have bothered to check if its weapons were loaded.
Zeta Halo's different structural design and usage of hexagonal pillars as underlying framework rather than shaped latticework makes sense when compared to the design of previous Halos seen (04,05); its the only one in the entire network that is of the original Senescent Array which were 30,000 km in diameter and much older (essentially making it a Generation 1 Halo). Installation 07/Zeta Halo had much of its diameter discarded in the past to bring it down in size to the newer Neoteric Array rings that were built after (Installations 01-06, the Generation 2 Halos).