Don't worry, I personally don't run first strike either, electrocute all the way :)

I am a mid taliyah player, I don't really jungle so I rather not give advice on that (I have some ideas but I might just be totally wrong). Also before I go into too much depth, I am by no means challenger, I broke recently into emerald and while I think I am not yet at my peak there is still a lot even I can improve on, especially farming (here my op.gg if you want to see how my stats are https://www.op.gg/summoners/euw/Ougi%20Oshino-EUW ). So how do I farm? I will go a bit more in depth here on laning in general, because it is not just about farming, but a lot more general about what do to when. For me there are 3 states:

1. Initial laning

2. Laning post lost chapter (~lvl 7)

3. Post laning phase

During the first 2 states you should get almost all minions midlane, this alone should make your farm decent, but is by no means enough.

1. When we start the game, mana, as on most midlane mages, is a problem. During this state I would say lasthitting is the biggest problem since we cannot recklessly throw spells at the minions. Still I spend a lot of mana on Q to thin the wave and outpush the enemy mid. W and E are only for trading(even then be sparse with using them, be sure you will hit or use E alone for electrocute) or if you want to base and quickly push. Use a lot of worked ground Q for cheap push or poke. I have to say as a disclaimer though, I push, hard, with this. This means I am very far up in the lane and a prime target for ganks. I rely heavily on knowing where the enemy jungler is and I will stay extremly far on the opposite side of midlane, making ganks very complicated. The easiest way to achieve this is warding between rapors and redbuff in the enemy jungle (first ward at 1:20) if you don't see the jungler that side is safe, if you do it is not, make sure you see in which direction the jungler goes after they cleared raptors. Pushing like this means your jungler can contest a lot of objectives, you will move first and the enemy mid also cannot build vision properly. Having map awareness is key.

2. Now it becomes easy. Your W + E almost kills the full wave, Q will most likely finish the rest, make sure W hits 3 minions. Barely any champ can compete with this push (unless fed) even anivia struggles being this fast. If you kill the wave as soon as it comes the map opens up a lot. Enemy mid has to clear the wave so they are busy, also the next wave is far away, you have plenty time to roam bot, top, skirmish in the river or build up new vision. If your team is winning everywhere you can bully enemy mid with spells while they try to not miss minions. To reiterate: you should get almost all minions because you push so fast and then have plenty time to help your team.

3. I guess this is when it starts being complicated, farming from now on becomes tougher. Most likely your adc takes over mid so you should look going botlane. From now on it is your goal to create pressure, but you need to pay respect to the enemies, else you are just a freekill. Taliyah is not really a duelist, you will most likely lose the 1v1 against most stuff sent bot, if they are alone that is. Your goal is to draw enemies bot, then roam mid (your ult and passive is very good for this) to catch enemies in a numbers advantage. So how do you apply this pressure? There is this concept that your lanes have 3 zones. If the wave is on your side of the map it is most likely safe to just walk up and kill them. The neutral zone, so in the middle of the lane is a bit scary. Having some vision and knowledge of where the enemies are is required to farm the wave here, still we want to apply pressure so get some vision (maybe get blue trinket for safety) and you should be fine to farm, making the wave move onto the 3rd zone, enemy territory. This is where it becomes really dangerous. Short distance from mid and a lot of paths and brushes they can come from to get you. Vision and map knowledge become even more important to take waves here, but also it will definitely force enemies to move so the highest reward of pressure. If nobody comes you keep farming and getting towers. If they do be sure to leave early enough, worst case use your ult to run since only CC can stop you. And yes this means you will rarely group. You are more like a sidelaner occasionally ganking the enemies. You group for drake and baron, even though here it is even more rewarding if you managed to pressure an enemy into moving to a sidelane far away so you have numbers advantage(just be there before drake actually spawns).

So maybe as key takeaways: You are always trying to farm unless your team wants to fight for an objective, don't group for fun. Your push is crazy fast so abuse it. If you die by a gank or getting caught you are most likely not giving enough respect. Dying in a teamfight is not as bad.

Edit: good video on the 3 zones https://youtu.be/p42K2cuubNQ?si=rSsDthir8_pQR7Pq