The key is to replicate the lightning lord (LL). In Genshin, Jing Yuan (JY) can have a passive where the LL deals damage say every 60s. By default it deals 3 hits of damage with say 100% scaling each (at lv10 Q). When JY uses E, it does an aoe slash that increases the LL hits per action by 2 while decreasing its cd by 15s. When JY uses Q, it does a larger aoe slash with higher scaling that increases the LL hits per action by 3 while decreasing its cd by 30s. The max hits per action is 10 (at c0). The E can have a 10s cd, and the Q can have 40-60 energy. Each hit by the LL can be an aoe blast strike on a random enemy within a certain range (say 10-20m). After the LL attacks, it resets to 3 hits per action, and the 60s timer restarts.
Similar to Raiden's chakra wheel, JY can have a wheel indicating how much time is left before the LL strikes (and perhaps also a counter indicating how many LL stacks he currently has). This chakra wheel can be on field all the time. Or if one wants, JY can summon chakra the first time the E is used with the LL starting with 3 stacks. The chakra will stay on field for 60s, after which it disappears if no E or Q is used. This can prevent the LL from randomly taking action in the middle of say quest dialogue.
Jing Yuan has a very simple design in HSR. His skill is aoe, his burst is aoe, his LL does blasts on random enemies. The LL is the thing with very high scaling, giving Jing Yuan high single target damage besides aoe damage.
In Genshin, one can add embellishments to the JY replica. Say his Q gives him electro infusion (for say 10s). When JY uses his NA, it can decrease the LL cd by 2s at a time (icd of 1s). Another passive allows his Q to reset the E cd. Or one can decrease the E cd by .6s for every stack the LL has.
C1 can give an extra charge on the E. C2 can increase the max number of stacks from 10 to 20. It can also make the LL start with 6 stacks by default rather than 3. C4 can increase JY's damage bonus by 5% for each stack LL has (up to 100%). C6 can make the LL have a 50% chance not to consume a stack every time it hits. Also when the LL has more than 10 stacks, it will do coordinated attacks with the active character every 2s. The scaling of this coordinated attack is 100% and increases by 10% for each additional stack above 10 (up to 200% scaling).
One can also have a passive/constellation that increases the number of stacks that the E and Q give (to say 4 and 6). Or when JY uses electro-infused NA, there is 20% chance to increase stacks of LL by 1 (icd of 1s).
Or when party members deal damage (use their NA/E/Q) they can increase the number of stacks of LL by 1. This way JY does not need to be on field all the time. Perhaps this is starting to sound familiar to Raiden.
Perhaps a 60s timer is too long, especially for things like spiral abyss. One can play around with the numbers. For example maybe 40s timer, E reduces cd by 10s, Q reduces cd by 20s. Or 30s timer, E reduce 7.5s, Q reduce 15s. Or if one wants to leave room for more stacks (up to 20): E reduce 3s, Q reduce 6s. Or maybe there is no need if there are other ways to obtain stacks via NA.
The LL is a kind of subdps that will proc even when JY is off-field. It does damage automatically and deterministically. So JY does not need to be like an on-field hypercarry.
But Jing Yuan has no equivalent in Genshin. The above kind of design with the LL would be unique among Genshin characters (as of version 3.8).
The LL damage could count as burst damage. Then emblem 4p could be bis. If JY is electro in Genshin, some EM could be worthwhile to proc aggravate with LL. But otherwise atk, electro dmg, crit are the main stats. A sacrificial weapon could help with E spam to gain more LL stacks. But most of JY's damage is from the LL, and the goal is to spam it as much as possible. The kit thus revolves around using E, Q, and NA to reduce the LL cd.
JY could work on any team as a subdps. JY would synergize with Raiden (for energy generation) and the usual suspects: Bennett, anemo vv (if JY is autumn element), Mona, etc.
The way JY charges up his LL to gain more stacks on a nuke is a similar idea to how Eula charges the nuke on her burst. The difference is that Eula requires energy to use her nuke, whereas JY can always nuke without energy.
E6 makes enemies more vulnerable up to 36%. This is essentially another 1.36 times multiplier to JY's damage. This is comparable to Yae Miko's C6, which ignores 60% def (~1.4 times multiplier to E), Raiden's C2, or Scaramouche's C6 (1.4 times multiplier to NA via additional scaling).
The difference is that JY's E6 is also multiplicative with def shred and scaling buffs (it is an extra multiplier on top of that). And for some reason, a lot of def shred appears to be more easily accessible in Star Rail. For example, just use Silver Wolf to reduce ~40% def, and JY's E6 will multiply on top of that for crazy multipliers.
To transfer JY's E6 to Genshin, one can either keep this extra 1.36 times multiplier or translate it into ignoring 60% def.
The new 1.5 follow-up dmg relic set (Ash Duke) in the Fyxestroll Garden is his new bis (for fua), a significant upgrade from the microaggression that was the original lightning set.
For supports: Tingyun, Ruan Mei work. Their buffs last enough to accomodate his fua turn order. Even Topaz can work as subdps support based on fua.
In HSR, things that buff fua include the Ash Duke relic set and Elation blessing in the SU.
Also, it appears the harmony units in HSR just give much greater buffs compared to Genshin counterparts.
At lv10 his fua does 66% + 25% atk scaling blast to a random target, up to 10 times. So it can do a total of (66+2*25)*10=1160% atk scaling. The max dps (or upper limit) of the fua (ignoring JY's E and Q) is then 1160 per turn (mv / damage per turn or dpt). This upper limit could technically be surpassed if the LL moves multiple times per turn (e.g. 0-cycle 2 actions). But usually moving 2-3 times per turn is a Seele kind of thing.
The way we do dps calcs for HSR is different from Genshin as unlike Genshin, HSR does not have 'time' or 'seconds' for 'damage per second' to make sense. Rather HSR has a sequence of events, being a turn-based game. But what is time if not the order of events, the flow of entropy, ...? Philosophical questions aside, in HSR we calculate dps based on damage per turn/cycle rather than damage per second.