I actually like the idea od Xayah jungle, but to me your build doesn't seem to have the best synergy with jungling.

I don't quite get why go full lifesteal.

1. grevious wounds is mandatory in most games, so you can get easily countered
2. shieldbow nerf
3. junglers need some form of early pressure so I'm pretty confident Galeforce would be the better choice for gank potential
4. anti-shields are trending now as well, among both assassins and mages
5. xayah doesn't normally build full sustain because other items are better and she doesn't need sustain to fight like a Samira does

yeah lifesteal will make you harder to kill but again, it is easily countered, dealys your spikes and makes you have less impact in game (which you should have as a jungler). Maybe if you just had better kiting items or burst you would not need the lifesteal

xayah might have CC but her CC is much weaker against enemies running away from her so I think having movement speed as a jungler is better. Maybe galeforce+PD+NQ for speed and utility? I normally build KS+PD+NQ and it has never lacked in damage and utility.

You don't need the lifesteal to jungle either, as in your first clear you were visibly healthy. Maybe only lacking a bit of damage (idk how good the damage got after first clear)

For Runes

I think fleet is better for the jungle as it gives movement speed and some small sustain in jungle. You will most likely never fully stack lethal tempo, I say that because I play Kindred and going for shorter burst trades is better for the role in my experience. Lethal tempo is for longer trades and you assume you will auto an enemy at least 6 times before they run away to their tower. Kindred has mobility and can't use this rune well in jungle, I doubt Xayah as an immobile zoning ADC can use this rune well in jungle. It barely works in lane.

If not fleet then HoB for shorter trades and quick root

I see you go overheal and pairs it up with sustain items. Again, doesn't look that important to me especially since you will build bloodthirster 2nd item (which seems a bit too expensive for a mid game powerspike in the jungle)... basically the rune will be useless for the rest of the game. And if you don't build lifesteal as I had suggested, the rune is also useless. Presence of mind is not needed because you get blue buff and mana sustain from camps.

So I think the best choice is actually Triumph as it help surviving skirmishes and teamfights.

Also, whether you go galeforce or Shieldbow, Ingenious Hunter is probably better than ravenous. Probably cosmic insight as well. Future's market to get earlier powerspikes. Nimbus cloak and celerity for ganking? You could go precision+domination, precision+inspiration, domination+inspiration

Also, maybe lethality could work since you get Youmuu's


For threats:

Definately assassins. I do consider xayah to be good into them, but alone in the jungle they are a much bigger threat than when you are an ADC. Probably take red smite against them and pray your team rotates.

Synergies

You put Nasus, Mundo and Cho as ideal syngergies but I don't think so. They are good because they are tanky but they lack good CC. Nasus and Mundo have slows, but I honestly think there are better synergies - like tanks and bruisers with hard cc. Maokai, Malphite, Leona, Volibear, Sett, Riven, even Irelia... also mages with CC like Syndra, Orianna, Veigar, Seraphine, Zyra, Morgana.

CC is nearly a must if you are an immobile jungler with a rather weak early game. Also, Xayah naturally does better with teams that have CC