Zhongli can be utilized as a Geo Burst damage dealer due to his short Burst cooldown (12s) and low energy cost (40 Energy). His Skill Hold Cast (Shield) scales with HP and at Ascension 4, you would unlock a talent that allows your Burst to scale with 33% of Zhongli's Max HP, making him a great source of Shield and damage. Though in certain teams without either very high investment into his damage or enough time in the rotation to burst without extending rotation times his burst can be a DPS loss.
Regarding Weapon Choices:
Lithic Spear: Assumes 3 stacks.
Blackcliff Pole: Assumes 0 stacks.
Favonius Lance: If the team values the particles from this weapon, then it can be better than all the other options mentioned for overall team damage (Note that you need to build some amount of CRIT Rate if you are running to trigger the passive)
Regarding Artifact Choices:
ATK% sands provides more damage than HP% sands, but it does have lesser Shield HP. If you want more Shield HP, you can consider running a HP% sands.
Sets
Archaic Petra (2): Combined with (2), on lower Energy Recharge requirements where Zhongli doesn't need to worry about his energy needs, this set pulls ahead of (4).
Noblesse Oblige (4): This set provides Zhongli more utility when casting his Burst, you can use this set on Zhongli if there is nobody else on the team who's equipping this set.
Tenacity of the Millelith (4): Just like (4), this set provides Zhongli with more utility if his Skill hits an enemy. This set also provides Zhongli with stronger shields.
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Indicates important notes at the bottom of the page.
This kind of playstyle is very straightforward; stack as much HP as possible. Prioritize HP scaling polearms such as and artifact sets such as (4) to capitalize on Zhongli's Shield. Most of the time, especially on a HP-focused Zhongli, casting Burst is a DPS loss due to the cast time, which is why you'd only want to cast Burst for the Crowd Control it offers, and not for damage.
Note that if paired with Xingqiu and/or Beidou, the damage reduction from orbitals from Xingqiu's Skill and Burst and/or Beidou's Burst can be utilized on Zhongli's shield, making it basically unbreakable.
Regarding Weapon Choices:
Favonius Lance: Use this weapon over if you value the team energy (Note that you need to build some amount of CRIT Rate if you are running to trigger the passive)
Regarding Artifact Choices:
Sets
Archaic Petra (4): Can be more useful than (4) in teams that don't scale as well with ATK buffs or already have another holder. Though it can be an awkward set to utilize well without extending rotation times, since the Holder of the set (Zhongli in this case) has to pickup the shard for the buff to take effect.
Scroll of the Hero of Cinder City (4): Preferred over if there are multiple Crystallize-compatible Elements or Geo characters that want DMG% bonus.
Deepwood Memories (4): This set works best in Dendro reaction focused teams (Bloom/Burgeon/Hyperbloom/Spread) that prefer having on Zhongli so that they can run more damage focused sets such as / instead for the highest overall damage gain. That said it means keeping the enemies near your pillars to have good uptime on the Dendro resistance shred effect, which can be difficult with no grouping abilities in a team.
Instructor (4): This set is usually only used in a few heavily reaction focused teams, such as Ganyu Melt or Hu Tao Vape, where you're maximising your damage in exchange for a weaker shield. Though Zhongli's shield is still usually more than strong enough even with fewer substat rolls to strengthen it.
Tenacity of the Millelith (4): This set is best in slot for Shield HP, but it's usually inconsistent against Bosses and needs good Construct placement, due to it's inconsistency, it's better to use other buffing sets that are mentioned if they work for the team.
Main Stats
CRIT Rate: Only recommended if using a Favonius weapon.