Not your fault. They have incompatible needs. It's just shit for a while. I felt exactly like that.
On the other hand, over time this is an important benefit of giving your eldest a sibling. She'll learn other people have needs that need to be considered.
To be brutal, you need to be less wobbly and a bit more practical. Guilt doesn't help anyone. Your DC needs you to be calm and clear. This is the new normal. She'll adapt. If you are upset you'll be inconsistent and that could be more unsettling for her.
Practically, can you bring forward the nursery start? Could your parents do little and often, eg take her out for an hour or two rather than a full day? Or they cd watch the baby so you can play with the toddler 121?
Have a routine including something to wear her out morning and afternoon, some quiet time, reading etc. When the baby's a bit bigger you can work in feeds and naps around this. My dc2 mainly napped in the sling so we cd go wherever.
Have a special bag/basket of toys just for nap and feed times, that she wants to play with but aren't noisy. DD used to love usborne dolly sticker books and wooden magnetic dress up dolls.
Give her a role to include her, eg sing a lullaby if the baby cries, bring a muslin for feeding, bring a baby toy. Get her a baby doll she can hold and burp etc.
If in doubt, go out. Even if it's ten mins round the block. It's sometimes claustrophobic at home and fresh air can reset the mood. Make it a snail count/bird watch/muddy puddle splash if you need to.
Make everything else easy as possible - hire a cleaner if you can afford it, use online shopping and have easy meals. Lower your standards!
It gets easier over time. Your baby will get used to some noise - I have videos of ds snoring away while my toddler plays with a tambourine two metres away! Good luck. You've been through a lot, be kind to yourself.