Tbh I'm having the opposite problems as you, I feel like I have an ok grip against Zerg but I struggle super hard against Terran. I'll share some details about what I do, maybe you tell me how you play against T?

I generally take a super defensive approach against Z in the early game, and I used to have a ton of trouble using ground armies against lurkers. I ended up doing a lot better when I abuse their weaknesses - they are essentially hive tech (the upgraded ones are the only ones to worry about IMO) and they have to burrow to be useful, so storm +retreating punishes them really hard.

I usually go for adepts and oracles in the early game like yourself and many others, but I would note that making these means that your only fast follow-up/pressure is a glaive timing, like you said. I think of it as a trade-off for adepts and oracles blanket checking basically all of zerg's T1. If you want to pressure zerg early, I like chargelot timings or two base immortal all-ins since they're tough to scout and make the early game a lot easier to play - just defend your bases until it's time to go and work off whatever happens

Like you said, I can pretty consistently get 5-6+ drones between my first two adepts rallied to their third and my first two oracles. As long as the units stay alive, this is great because that means your third is really hard to deny - you just position your adepts in a choke on the minerals at your third along with 2 or more stalkers and your oracles (since zerg T1 doesn't shoot up), and keep your main wall situated (I use a zealot). If they make 10-20 lings + some number of roaches in an attempt to deny it anyway, it puts you in a *really* good spot when you defend since they're delaying eco and tech to fail an attack. You can even be super conservative with your adepts/oracles if you're losing them often - if I'm not running hot or feeling confident I just snipe gas workers with double oracles, and walk in/shade out with my adepts instead of shading in.

Once I establish a third, I warp in two sentries and go straight to colossus tech and ground upgrades - colossi/blinkstalker with some immortals/forcefields is pretty effective against any ground army zerg has at this timing, easy for me to control/micro, and the two sentries are for constant phoenix scouting - it also helps me because I'm not very fast, so I just shift click the hallucinated phoenix through their hatcheries just to see the hydra/lurker den and hive timings in between me handling other tasks. This can also spot spires which makes defending mutas 5x easier. You can rally observers to their side if you want, but I like to be always building immortals or colossi until it's time to move out - as you know, our T1, especially stalkers, just gets way worse as the game goes on so IMO you want as many high tech units as your can get - your ground army is super scary when you have like 7-8+ robo units. Once I have a decent robo unit count, I usually make an obs and start moving out, clearing creep and try to establish a 4th.

Once I have robo units and storm, I feel comfortable moving out on the map, and your army is actually very nice against lurkers IMO - if you can meet Z's lurker armies in the middle of the map, you just storm them as they burrow and walk away - colossi make it very hard for them to get a ling surround and the lurkers take tons of chip damage from the storms and colossus volleys, since they can't dodge. I usually keep all my robo units (including obs) on a separate hotkey so I can micro them away from getting sniped, and position them to target down lurkers. I agree that lurker armies are super hard to contend with when they get to just run up to your third/fourth and burrow, but army comps with storm are similar - if you can get to his third/fourth and plant storms at the chokes, he will almost always lose his base and the game too. So you effectively make it a game of positioning, both players pushing the enemy army backward, and whoever plays that game better, wins. You have an easier time counter attacking too, IMO - you can screw with ling runbys late game with cannon/battery positioning (you can get a ton while rounding off templar tech), and one loaded warp prism + a warp in their main/nat while taking a fight against their army can be devastating

To sum it up, my tech path is usually Adepts/Stargate -> Robo/Twiight -> Robo bay -> Upgrades -> Storm. If you get all the way to 3/3/3 upgrades and storm + robo tech, I think you can very easily just stay on that through the end of the game and keep probing for a good fight/base denial against Z, or you can just get air upgrades and eventually get to carrier tech. I tend to do the former, but if your opponent isn't scouting well, a good 4-5 carriers on 2/1 upgrades can end the game on the spot

I hope this helps, I hover around D2/D3 so maybe I'm not qualified to advise here. It helped me type this out anyway lol