Hello again! I’ll try and answer your questions.
1. Bronzong’s Moveset
Referring to Pikalytics, almost all Bronzong run trick room (98.9%), so it’s primarily a trick room setter. It’s next most used move is Body Press, which allows it to not have to invest in attack. You can also use Iron Defense to further boost its power. Gyro Ball is up there like you mentioned, but after Body Press comes Bulldoze. This has been seen on a lot of trick room setters in 2020 to proc a weakness policy on the team’s sweeper. Other things you can do with Bronzong are dual screen support, steel roller to get rid of psyspam/Rillaboom, and Ally Switch shenanigans.
2. Viability as a Trick Room Setter
The two most popular trick room setters right now are dusclops and Porygon-2, both of which have more bulk than Bronzong. Plus, dusclops has basically the same utility as Bronzong- Trick room, weakness policy proc, ally switch and general annoyance, plus better bulk. However, Bronzong has access to his item slot, so it can use mental herbs/resistance berries to further help trick room go up. Not to mention his 2 immunities to ground and poison.
3. Good Teammates for Bronzong
To recap question 2, Bronzong is good for weakness policy Pokemon, slow Pokémon, and Pokémon with powerful all-target ground/poison moves.
With all this, I’d say he could be a good partner for Rhyperior (and Steelix, but it’s not as powerful) to proc weakness policy and allow free earthquakes, and dragalge, to similarly proc weakness policy and allow free sludge waves. I’d argued that Bronzong is not a good teammate for hatterene as it’s already a trick room setter, so you’re better off with the usual hatterene+ indeedee support.
4. Bronzong’s viability in 2020
I didn’t play back in 2016, but I understand that it was most likely popular because of groudon, because it could switch into a precipice blades for free. However, there’s no groudon anymore! Ground is a good type, but just not overused enough to justify using Bronzong over bulkier options like dusclops and Porygon2. There are some niche roles for it, however, like if you’re worried about taunt/Strong ghost/dark type attacks, it can be better than the eviolite users because of its item slot. In addition, it’s not as passive as dusclops offensively because of body press. It is also good with Rhyperior/Dragalgae, vas I mentioned.
Overall, Bronzong is a solid Trick Room setter that’s usually outclassed by bulkier options, but it has some niche roles.
Hope I helped!