First of all- you’re not a crappy mum, it is HARD, I have a toddler & a new baby, so I know what you mean! Could you try setting up some safe toddler play activities/trays/cupboards so that you can redirect to something when you’re feeding/busy with baby? That’s one of the main things I do which really helps, every night before I go to bed I just set up a really quick activity or toy basket full of random things (think some feathers, wooden kitchen spoon, toilet roll tube etc doesn’t have to be fancy) so that in the morning my daughter spots that and it buys me some time! Or activities like colouring, stickers, crafts, I sit on the floor and do with my toddler while baby feeds.
I’d also say where possible try to find pockets in the day for quality time dedicated to your eldest- even 10 mins of 1-1 time “fills their cup” more than an hour of shared time. I tend to get baby napping in the moses basket and then sit and play solely with toddler for as long as the nap lasts basically, or if baby won’t settle in the moses basket I pop him in the sling for his nap and play with my toddler and focus just on her- housework can wait, let the admin slip a bit.
Another thing depending on what is available near you, activities or groups for your toddler to run off some energy, bonus points if timed for a baby nap so you can join in! We go to a church playgroup one morning a week, baby in sling, so I can run around and play with her, another day we will go to the park (even in the rain, coats/puddle suits on and go, it helps!) and again just let them burn off some steam, we have a local sensory playroom which I’ve done a few times so toddler can play and baby can just watch & be equally entertained, toddler groups are fab for this too, entertainment and playtime for them to fill their cup while you watch.
It won’t last forever, you get through it however you can. You’re doing a good job, it’s just a really hard job!